diff --git a/slowCheck/src/slowCheck/CounterExampleImpl.java b/slowCheck/src/slowCheck/CounterExampleImpl.java
new file mode 100644
index 000000000000..71a6ed268720
--- /dev/null
+++ b/slowCheck/src/slowCheck/CounterExampleImpl.java
@@ -0,0 +1,41 @@
+package slowCheck;
+
+import org.jetbrains.annotations.Nullable;
+
+import java.util.function.Predicate;
+
+class CounterExampleImpl<T> implements PropertyFailure.CounterExample<T> {
+  final StructureNode data;
+  private final T value;
+  @Nullable private final Throwable exception;
+
+  private CounterExampleImpl(StructureNode data, T value, @Nullable Throwable exception) {
+    this.data = data;
+    this.value = value;
+    this.exception = exception;
+  }
+
+  @Override
+  public T getExampleValue() {
+    return value;
+  }
+
+  @Nullable
+  @Override
+  public Throwable getExceptionCause() {
+    return exception;
+  }
+
+  static <T> CounterExampleImpl<T> checkProperty(Predicate<T> property, T value, StructureNode node) {
+    try {
+      if (!property.test(value)) {
+        return new CounterExampleImpl<>(node, value, null);
+      }
+    }
+    catch (Throwable e) {
+      return new CounterExampleImpl<>(node, value, e);
+    }
+    return null;
+  }
+
+}
\ No newline at end of file
diff --git a/slowCheck/src/slowCheck/DataStructure.java b/slowCheck/src/slowCheck/DataStructure.java
index 22568f204285..163e5aacd578 100644
--- a/slowCheck/src/slowCheck/DataStructure.java
+++ b/slowCheck/src/slowCheck/DataStructure.java
@@ -14,7 +14,12 @@ public interface DataStructure {
   }
   
   int drawInt(@NotNull IntDistribution distribution);
-  
+
+  /**
+   * @return a non-negative number used by various generators to guide the sizes of structures (e.g. collections) they create.
+   * The sizes need not be exactly equal to this hint, but in average bigger hints should in average correspond to bigger structures. When generators invoke other generators using {@link #subStructure}, the size hint of the sub-structure is
+   * generally less than the parent's one.
+   */
   int getSizeHint();
   
   default int suggestCollectionSize() {
diff --git a/slowCheck/src/slowCheck/GeneratorException.java b/slowCheck/src/slowCheck/GeneratorException.java
index 6cc9ea143a50..4e5c289a9a30 100644
--- a/slowCheck/src/slowCheck/GeneratorException.java
+++ b/slowCheck/src/slowCheck/GeneratorException.java
@@ -5,7 +5,7 @@ package slowCheck;
  */
 public class GeneratorException extends RuntimeException {
 
-  GeneratorException(long seed, Throwable cause) {
-    super("Exception while generating data, seed=" + seed, cause);
+  GeneratorException(Iteration<?> iteration, Throwable cause) {
+    super("Exception while generating data, " + iteration.printSeeds(), cause);
   }
 }
diff --git a/slowCheck/src/slowCheck/Iteration.java b/slowCheck/src/slowCheck/Iteration.java
new file mode 100644
index 000000000000..5ec409fda6f7
--- /dev/null
+++ b/slowCheck/src/slowCheck/Iteration.java
@@ -0,0 +1,110 @@
+package slowCheck;
+
+import org.jetbrains.annotations.Nullable;
+
+import java.util.HashSet;
+import java.util.Random;
+import java.util.Set;
+import java.util.function.IntUnaryOperator;
+import java.util.function.Predicate;
+
+class Iteration<T> {
+
+  private static final Predicate<Object> DATA_IS_DIFFERENT = new Predicate<Object>() {
+    @Override
+    public boolean test(Object o) {
+      return false;
+    }
+
+    @Override
+    public String toString() {
+      return ": cannot generate enough sufficiently different values";
+    }
+  };
+
+  final CheckSession<T> session;
+  final long iterationSeed;
+  final int sizeHint;
+  final int iterationNumber;
+
+  Iteration(CheckSession<T> session, long iterationSeed, int iterationNumber) {
+    this.session = session;
+    this.iterationSeed = iterationSeed;
+    this.sizeHint = session.sizeHintFun.applyAsInt(iterationNumber);
+    this.iterationNumber = iterationNumber;
+    if (sizeHint < 0) {
+      throw new IllegalArgumentException("Size hint should be non-negative, found " + sizeHint);
+    }
+  }
+
+  @Nullable
+  private CounterExampleImpl<T> findCounterExample(Random random) {
+    for (int i = 0; i < 100; i++) {
+      StructureNode node = new StructureNode();
+      T value;
+      try {
+        value = session.generator.getGeneratorFunction().apply(new GenerativeDataStructure(random, node, sizeHint));
+      }
+      catch (Throwable e) {
+        throw new GeneratorException(this, e);
+      }
+      if (!session.generatedHashes.add(node.hashCode())) continue;
+
+      return CounterExampleImpl.checkProperty(session.property, value, node);
+    }
+    throw new CannotSatisfyCondition(DATA_IS_DIFFERENT);
+  }
+
+  String printToReproduce() {
+    return "To reproduce the last iteration, run PropertyChecker.forAll(...).rechecking(" + iterationSeed + "L, " + sizeHint + ").shouldHold(...)\n" +
+           "Global seed: " + session.globalSeed + "L";
+  }
+
+  String printSeeds() {
+    return "iteration seed=" + iterationSeed + "L, " +
+           "size hint=" + sizeHint + ", " +
+           "global seed=" + session.globalSeed + "L";
+  }
+
+  @Nullable
+  Iteration<T> performIteration() {
+    session.notifier.iterationStarted(iterationNumber);
+
+    Random random = new Random(iterationSeed);
+    CounterExampleImpl<T> example = findCounterExample(random);
+    if (example != null) {
+      session.notifier.counterExampleFound(this);
+      PropertyFailureImpl<T> failure = new PropertyFailureImpl<>(example, this);
+      throw new PropertyFalsified(failure, () -> new ReplayDataStructure(failure.getMinimalCounterexample().data, sizeHint));
+    }
+
+    if (iterationNumber >= session.iterationCount) {
+      return null;
+    }
+    
+    return new Iteration<>(session, random.nextLong(), iterationNumber + 1);
+  }
+}
+
+class CheckSession<T> {
+  final Generator<T> generator;
+  final Predicate<T> property;
+  final long globalSeed;
+  final Set<Integer> generatedHashes = new HashSet<>();
+  final StatusNotifier notifier;
+  final int iterationCount;
+  final IntUnaryOperator sizeHintFun;
+
+  CheckSession(Generator<T> generator, Predicate<T> property, long globalSeed, int iterationCount, IntUnaryOperator sizeHintFun) {
+    this.generator = generator;
+    this.property = property;
+    this.globalSeed = globalSeed;
+    this.iterationCount = iterationCount;
+    this.sizeHintFun = sizeHintFun;
+    notifier = new StatusNotifier(iterationCount);
+  }
+
+  Iteration<T> firstIteration() {
+    return new Iteration<>(this, globalSeed, 1);
+  }
+}
diff --git a/slowCheck/src/slowCheck/PropertyChecker.java b/slowCheck/src/slowCheck/PropertyChecker.java
index d6e49b809193..4746c262d450 100644
--- a/slowCheck/src/slowCheck/PropertyChecker.java
+++ b/slowCheck/src/slowCheck/PropertyChecker.java
@@ -1,201 +1,81 @@
 package slowCheck;
 
 import org.jetbrains.annotations.NotNull;
-import org.jetbrains.annotations.Nullable;
 
-import java.util.HashSet;
 import java.util.Random;
-import java.util.Set;
+import java.util.function.IntUnaryOperator;
 import java.util.function.Predicate;
 
 /**
- * @author peter
+ * An entry point to property-based testing. The main usage pattern: {@code PropertyChecker.forAll(generator).shouldHold(property)}.
  */
 public class PropertyChecker<T> {
-  private static final Predicate<Object> DATA_IS_DIFFERENT = new Predicate<Object>() {
-    @Override
-    public boolean test(Object o) {
-      return false;
-    }
-
-    @Override
-    public String toString() {
-      return ": cannot generate enough sufficiently different values";
-    }
-  };
   private final Generator<T> generator;
-  private Predicate<T> property;
-  private final Set<Integer> generatedHashes = new HashSet<>();
-  private long seed = new Random().nextLong();
+  private long globalSeed = new Random().nextLong();
+  private IntUnaryOperator sizeHintFun = iteration -> (iteration - 1) % 100 + 1;
   private int iterationCount = 100;
-  private StatusNotifier notifier;
 
   private PropertyChecker(Generator<T> generator) {
     this.generator = generator;
   }
 
+  /**
+   * Creates a property checker for the given generator. It can be further customized using {@code with*}-methods, 
+   * and should finally used for property to check via {@link #shouldHold(Predicate)} call.
+   */
   public static <T> PropertyChecker<T> forAll(Generator<T> generator) {
     return new PropertyChecker<>(generator);
   }
-  
+
+  /**
+   * This function allows to start the test with a fixed random seed. It's useful to reproduce some previous test run and debug it.
+   * @param seed A random seed to use for the first iteration.
+   *             The following iterations will use other, pseudo-random seeds, but still derived from this one.
+   * @return this PropertyChecker
+   */
   public PropertyChecker<T> withSeed(long seed) {
-    this.seed = seed;
+    globalSeed = seed;
     return this;
   }
 
+  /**
+   * @param iterationCount the number of iterations to try. By default it's 100.
+   * @return this PropertyChecker
+   */
   public PropertyChecker<T> withIterationCount(int iterationCount) {
     this.iterationCount = iterationCount;
     return this;
   }
 
+  /**
+   * @param sizeHintFun a function determining how size hint should be distributed depending on the iteration number.
+   *                    By default the size hint will be 1 in the first iteration, 2 in the second one, and so on until 100,
+   *                    then again 1,...,100,1,...,100, etc.
+   * @return this PropertyChecker
+   * @see DataStructure#getSizeHint() 
+   */
+  public PropertyChecker<T> withSizeHint(@NotNull IntUnaryOperator sizeHintFun) {
+    this.sizeHintFun = sizeHintFun;
+    return this;
+  }
+
+  /**
+   * Checks the property within a single iteration by using specified seed and size hint. Useful to debug the test after it's failed.
+   */
+  public PropertyChecker<T> rechecking(long seed, int sizeHint) {
+    return withSeed(seed).withSizeHint(whatever -> sizeHint).withIterationCount(1);
+  }
+
+  /**
+   * Checks that the given property returns {@code true} and doesn't throw exceptions by running the generator and the property
+   * given number of times (see {@link #withIterationCount(int)}).
+   */
   public void shouldHold(@NotNull Predicate<T> property) {
-    if (this.property != null) throw new IllegalArgumentException("Property " + property + " already checked");
-    this.property = property;
-    notifier = new StatusNotifier(iterationCount, this.seed);
-    
-    Random random = new Random(seed);
-    
-    for (int i = 1; i <= iterationCount; i++) {
-      notifier.iterationStarted(i);
-
-      CounterExampleImpl<T> example = findCounterExample(i, random);
-      if (example != null) {
-        notifier.counterExampleFound();
-        PropertyFailureImpl failure = new PropertyFailureImpl(example, i);
-        throw new PropertyFalsified(seed, failure, () -> new ReplayDataStructure(failure.getMinimalCounterexample().data, failure.sizeHint));
-      }
+    Iteration<T> iteration = new CheckSession<>(generator, property, globalSeed, iterationCount, sizeHintFun).firstIteration();
+    while (iteration != null) {
+      iteration = iteration.performIteration();
     }
   }
 
-  @Nullable
-  private CounterExampleImpl<T> findCounterExample(int sizeHint, Random random) {
-    for (int i = 0; i < 100; i++) {
-      StructureNode node = new StructureNode();
-      T value;
-      try {
-        value = generator.getGeneratorFunction().apply(new GenerativeDataStructure(random, node, sizeHint));
-      }
-      catch (Throwable e) {
-        throw new GeneratorException(seed, e);
-      }
-      if (!generatedHashes.add(node.hashCode())) continue;
-      
-      return CounterExampleImpl.checkProperty(property, value, node);
-    }
-    throw new CannotSatisfyCondition(DATA_IS_DIFFERENT);
-  }
-
-  private class PropertyFailureImpl implements PropertyFailure<T> {
-    private final CounterExampleImpl<T> initial;
-    private CounterExampleImpl<T> minimized;
-    private int totalSteps;
-    private int successfulSteps;
-    private int sizeHint;
-    private Throwable stoppingReason;
-
-    PropertyFailureImpl(@NotNull CounterExampleImpl<T> initial, int sizeHint) {
-      this.initial = initial;
-      this.minimized = initial;
-      this.sizeHint = sizeHint;
-      try {
-        shrink();
-      }
-      catch (Throwable e) {
-        stoppingReason = e;
-      }
-    }
-
-    @NotNull
-    @Override
-    public CounterExampleImpl<T> getFirstCounterExample() {
-      return initial;
-    }
-
-    @NotNull
-    @Override
-    public CounterExampleImpl<T> getMinimalCounterexample() {
-      return minimized;
-    }
-
-    @Nullable
-    @Override
-    public Throwable getStoppingReason() {
-      return stoppingReason;
-    }
-
-    @Override
-    public int getTotalMinimizationExampleCount() {
-      return totalSteps;
-    }
-
-    @Override
-    public int getMinimizationStageCount() {
-      return successfulSteps;
-    }
-
-    private void shrink() {
-      ShrinkRunner shrinkRunner = new ShrinkRunner();
-      while (true) {
-        CounterExampleImpl<T> shrank = shrinkRunner.findShrink(minimized.data, node -> {
-          if (!generatedHashes.add(node.hashCode())) return null;
-
-          notifier.shrinkAttempt(this);
-          
-          try {
-            T value = generator.getGeneratorFunction().apply(new ReplayDataStructure(node, sizeHint));
-            totalSteps++;
-            return CounterExampleImpl.checkProperty(property, value, node);
-          }
-          catch (CannotRestoreValue e) {
-            return null;
-          }
-        });
-        if (shrank != null) {
-          minimized = shrank;
-          successfulSteps++;
-        } else {
-          break;
-        }
-      }
-    }
-
-
-  }
-}
-
-class CounterExampleImpl<T> implements PropertyFailure.CounterExample<T> {
-  final StructureNode data;
-  private final T value;
-  @Nullable private final Throwable exception;
-
-  private CounterExampleImpl(StructureNode data, T value, @Nullable Throwable exception) {
-    this.data = data;
-    this.value = value;
-    this.exception = exception;
-  }
-
-  @Override
-  public T getExampleValue() {
-    return value;
-  }
-
-  @Nullable
-  @Override
-  public Throwable getExceptionCause() {
-    return exception;
-  }
-
-  static <T> CounterExampleImpl<T> checkProperty(Predicate<T> property, T value, StructureNode node) {
-    try {
-      if (!property.test(value)) {
-        return new CounterExampleImpl<>(node, value, null);
-      }
-    }
-    catch (Throwable e) {
-      return new CounterExampleImpl<>(node, value, e);
-    }
-    return null;
-  }
-
 }
 
diff --git a/slowCheck/src/slowCheck/PropertyFailure.java b/slowCheck/src/slowCheck/PropertyFailure.java
index 60f215c26cab..17df0b502333 100644
--- a/slowCheck/src/slowCheck/PropertyFailure.java
+++ b/slowCheck/src/slowCheck/PropertyFailure.java
@@ -19,6 +19,14 @@ public interface PropertyFailure<T> {
   int getTotalMinimizationExampleCount();
   
   int getMinimizationStageCount();
+  
+  int getIterationNumber();
+  
+  long getIterationSeed();
+  
+  long getGlobalSeed();
+  
+  int getSizeHint();
 
   interface CounterExample<T> {
     T getExampleValue();
diff --git a/slowCheck/src/slowCheck/PropertyFailureImpl.java b/slowCheck/src/slowCheck/PropertyFailureImpl.java
new file mode 100644
index 000000000000..9f1c077c8200
--- /dev/null
+++ b/slowCheck/src/slowCheck/PropertyFailureImpl.java
@@ -0,0 +1,100 @@
+package slowCheck;
+
+import org.jetbrains.annotations.NotNull;
+import org.jetbrains.annotations.Nullable;
+
+class PropertyFailureImpl<T> implements PropertyFailure<T> {
+  private final CounterExampleImpl<T> initial;
+  private CounterExampleImpl<T> minimized;
+  private int totalSteps;
+  private int successfulSteps;
+  final Iteration<T> iteration;
+  private Throwable stoppingReason;
+
+  PropertyFailureImpl(@NotNull CounterExampleImpl<T> initial, Iteration<T> iteration) {
+    this.initial = initial;
+    this.minimized = initial;
+    this.iteration = iteration;
+    try {
+      shrink();
+    }
+    catch (Throwable e) {
+      stoppingReason = e;
+    }
+  }
+
+  @NotNull
+  @Override
+  public CounterExampleImpl<T> getFirstCounterExample() {
+    return initial;
+  }
+
+  @NotNull
+  @Override
+  public CounterExampleImpl<T> getMinimalCounterexample() {
+    return minimized;
+  }
+
+  @Nullable
+  @Override
+  public Throwable getStoppingReason() {
+    return stoppingReason;
+  }
+
+  @Override
+  public int getTotalMinimizationExampleCount() {
+    return totalSteps;
+  }
+
+  @Override
+  public int getMinimizationStageCount() {
+    return successfulSteps;
+  }
+
+  @Override
+  public int getIterationNumber() {
+    return iteration.iterationNumber;
+  }
+
+  @Override
+  public long getIterationSeed() {
+    return iteration.iterationSeed;
+  }
+
+  @Override
+  public long getGlobalSeed() {
+    return iteration.session.globalSeed;
+  }
+
+  @Override
+  public int getSizeHint() {
+    return iteration.sizeHint;
+  }
+
+  private void shrink() {
+    ShrinkRunner shrinkRunner = new ShrinkRunner();
+    while (true) {
+      CounterExampleImpl<T> shrank = shrinkRunner.findShrink(minimized.data, node -> {
+        if (!iteration.session.generatedHashes.add(node.hashCode())) return null;
+
+        iteration.session.notifier.shrinkAttempt(this, iteration);
+
+        try {
+          T value = iteration.session.generator.getGeneratorFunction().apply(new ReplayDataStructure(node, iteration.sizeHint));
+          totalSteps++;
+          return CounterExampleImpl.checkProperty(iteration.session.property, value, node);
+        }
+        catch (CannotRestoreValue e) {
+          return null;
+        }
+      });
+      if (shrank != null) {
+        minimized = shrank;
+        successfulSteps++;
+      }
+      else {
+        break;
+      }
+    }
+  }
+}
diff --git a/slowCheck/src/slowCheck/PropertyFalsified.java b/slowCheck/src/slowCheck/PropertyFalsified.java
index ec8803ed2bad..c4a6fa239693 100644
--- a/slowCheck/src/slowCheck/PropertyFalsified.java
+++ b/slowCheck/src/slowCheck/PropertyFalsified.java
@@ -11,13 +11,11 @@ import java.util.function.Supplier;
 public class PropertyFalsified extends RuntimeException {
   static final String FAILURE_REASON_HAS_CHANGED_DURING_MINIMIZATION = "!!! FAILURE REASON HAS CHANGED DURING MINIMIZATION !!!";
   private static final String SEPARATOR = "\n==========================\n";
-  private final long seed;
-  private final PropertyFailure<?> failure;
+  private final PropertyFailureImpl<?> failure;
   private final Supplier<DataStructure> data;
 
-  PropertyFalsified(long seed, PropertyFailure<?> failure, Supplier<DataStructure> data) {
+  PropertyFalsified(PropertyFailureImpl<?> failure, Supplier<DataStructure> data) {
     super(failure.getMinimalCounterexample().getExceptionCause());
-    this.seed = seed;
     this.failure = failure;
     this.data = data;
   }
@@ -26,7 +24,7 @@ public class PropertyFalsified extends RuntimeException {
   public String getMessage() {
     String msg = "Falsified on " + failure.getMinimalCounterexample().getExampleValue() + "\n" +
                  getMinimizationStats() +
-                 "Seed=" + seed;
+                 failure.iteration.printToReproduce();
 
     if (failure.getStoppingReason() != null) {
       msg += "\n Shrinking stopped because of " + StatusNotifier.printStackTrace(failure.getStoppingReason());
diff --git a/slowCheck/src/slowCheck/StatusNotifier.java b/slowCheck/src/slowCheck/StatusNotifier.java
index d9122682aa47..ddf3825bcbe6 100644
--- a/slowCheck/src/slowCheck/StatusNotifier.java
+++ b/slowCheck/src/slowCheck/StatusNotifier.java
@@ -15,13 +15,11 @@ import java.util.Locale;
 @SuppressWarnings("UseOfSystemOutOrSystemErr")
 class StatusNotifier {
   private final int iterationCount;
-  private final long seed;
   private int currentIteration;
   private long lastPrinted = System.currentTimeMillis();
 
-  StatusNotifier(int iterationCount, long seed) {
+  StatusNotifier(int iterationCount) {
     this.iterationCount = iterationCount;
-    this.seed = seed;
   }
 
   void iterationStarted(int iteration) {
@@ -31,9 +29,9 @@ class StatusNotifier {
     }
   }
 
-  void counterExampleFound() {
+  void counterExampleFound(Iteration<?> iteration) {
     lastPrinted = System.currentTimeMillis();
-    System.err.println(formatCurrentTime() + ": failed on iteration " + currentIteration + " (seed=" + seed + "), shrinking...");
+    System.err.println(formatCurrentTime() + ": failed on iteration " + currentIteration + " (" + iteration.printSeeds() + "), shrinking...");
   }
 
   private boolean shouldPrint() {
@@ -46,11 +44,11 @@ class StatusNotifier {
 
   private int lastReportedStage = -1;
   private String lastReportedTrace = null;
-  void shrinkAttempt(PropertyFailure<?> failure) {
+  <T> void shrinkAttempt(PropertyFailure<T> failure, Iteration<T> iteration) {
     if (shouldPrint()) {
       int stage = failure.getMinimizationStageCount();
-      System.err.println(formatCurrentTime() + ": still shrinking (seed=" + seed + "). " +
-                         "Examples tried: " + failure.getTotalMinimizationExampleCount() + 
+      System.out.println(formatCurrentTime() + ": still shrinking (" + iteration.printSeeds() + "). " +
+                         "Examples tried: " + failure.getTotalMinimizationExampleCount() +
                          ", successful minimizations: " + stage);
       if (lastReportedStage != stage) {
         lastReportedStage = stage;
diff --git a/slowCheck/test/slowCheck/ExceptionTest.java b/slowCheck/test/slowCheck/ExceptionTest.java
index 18f37d885751..8a4333333850 100644
--- a/slowCheck/test/slowCheck/ExceptionTest.java
+++ b/slowCheck/test/slowCheck/ExceptionTest.java
@@ -8,44 +8,30 @@ import static slowCheck.Generator.*;
 public class ExceptionTest extends PropertyCheckerTestCase {
 
   public void testFailureReasonUnchanged() {
-    try {
-      forAllStable(integers()).shouldHold(i -> {
-        throw new AssertionError("fail");
-      });
-      fail();
-    }
-    catch (PropertyFalsified e) {
-      assertFalse(e.getMessage().contains(PropertyFalsified.FAILURE_REASON_HAS_CHANGED_DURING_MINIMIZATION));
-    }
+    PropertyFalsified e = checkFails(forAllStable(integers()), i -> {
+      throw new AssertionError("fail");
+    });
+
+    assertFalse(e.getMessage().contains(PropertyFalsified.FAILURE_REASON_HAS_CHANGED_DURING_MINIMIZATION));
   }
 
   public void testFailureReasonChangedExceptionClass() {
-    try {
-      forAllStable(integers()).shouldHold(i -> {
-        throw (i == 0 ? new RuntimeException("fail") : new IllegalArgumentException("fail"));
-      });
-      fail();
-    }
-    catch (PropertyFalsified e) {
-      assertTrue(e.getMessage().contains(PropertyFalsified.FAILURE_REASON_HAS_CHANGED_DURING_MINIMIZATION));
-    }
+    PropertyFalsified e = checkFails(forAllStable(integers()), i -> {
+      throw (i == 0 ? new RuntimeException("fail") : new IllegalArgumentException("fail"));
+    });
+    assertTrue(e.getMessage().contains(PropertyFalsified.FAILURE_REASON_HAS_CHANGED_DURING_MINIMIZATION));
   }
 
   public void testFailureReasonChangedExceptionTrace() {
-    try {
-      forAllStable(integers()).shouldHold(i -> {
-        if (i == 0) {
-          throw new AssertionError("fail");
-        }
-        else {
-          throw new AssertionError("fail2");
-        }
-      });
-      fail();
-    }
-    catch (PropertyFalsified e) {
-      assertTrue(e.getMessage().contains(PropertyFalsified.FAILURE_REASON_HAS_CHANGED_DURING_MINIMIZATION));
-    }
+    PropertyFalsified e = checkFails(forAllStable(integers()), i -> {
+      if (i == 0) {
+        throw new AssertionError("fail");
+      }
+      else {
+        throw new AssertionError("fail2");
+      }
+    });
+    assertTrue(e.getMessage().contains(PropertyFalsified.FAILURE_REASON_HAS_CHANGED_DURING_MINIMIZATION));
   }
 
   public void testExceptionWhileGeneratingValue() {
@@ -60,17 +46,13 @@ public class ExceptionTest extends PropertyCheckerTestCase {
   }
 
   public void testExceptionWhileShrinkingValue() {
-    try {
-      forAllStable(listsOf(integers()).suchThat(l -> {
-        if (l.size() == 1 && l.get(0) == 0) throw new RuntimeException("my exception");
-        return true;
-      })).shouldHold(l -> l.stream().allMatch(i -> i > 0));
-      fail();
-    }
-    catch (PropertyFalsified e) {
-      assertEquals("my exception", e.getFailure().getStoppingReason().getMessage());
-      assertTrue(StatusNotifier.printStackTrace(e).contains("my exception"));
-    }
+    PropertyFalsified e = checkFails(PropertyChecker.forAll(listsOf(integers()).suchThat(l -> {
+      if (l.size() == 1 && l.get(0) == 0) throw new RuntimeException("my exception");
+      return true;
+    })), l -> l.stream().allMatch(i -> i > 0));
+
+    assertEquals("my exception", e.getFailure().getStoppingReason().getMessage());
+    assertTrue(StatusNotifier.printStackTrace(e).contains("my exception"));
   }
 
   public void testUnsatisfiableSuchThat() {
diff --git a/slowCheck/test/slowCheck/GeneratorTest.java b/slowCheck/test/slowCheck/GeneratorTest.java
index e73c948eef70..cdc01781ba2f 100644
--- a/slowCheck/test/slowCheck/GeneratorTest.java
+++ b/slowCheck/test/slowCheck/GeneratorTest.java
@@ -4,6 +4,7 @@ import java.util.ArrayList;
 import java.util.HashSet;
 import java.util.List;
 import java.util.Set;
+import java.util.function.Predicate;
 import java.util.stream.Collectors;
 
 import static slowCheck.Generator.*;
@@ -28,25 +29,25 @@ public class GeneratorTest extends PropertyCheckerTestCase {
   public void testListContainsDivisible() {
     checkFalsified(nonEmptyLists(integers()),
                    l -> l.stream().allMatch(i -> i % 10 != 0),
-                   9);
+                   3);
   }
 
   public void testStringContains() {
     checkFalsified(stringsOf(asciiPrintableChars()),
                    s -> !s.contains("a"),
-                   10);
+                   7);
   }
 
   public void testLetterStringContains() {
     checkFalsified(stringsOf(asciiLetters()),
                    s -> !s.contains("a"),
-                   5);
+                   3);
   }
   
   public void testIsSorted() {
     PropertyFailure<List<Integer>> failure = checkFalsified(nonEmptyLists(integers()),
                                                             l -> l.stream().sorted().collect(Collectors.toList()).equals(l),
-                                                            69);
+                                                            67);
     assertEquals(2, failure.getMinimalCounterexample().getExampleValue().size());
   }
 
@@ -57,7 +58,7 @@ public class GeneratorTest extends PropertyCheckerTestCase {
   public void testSortedDoublesNonDescending() {
     PropertyFailure<List<Double>> failure = checkFalsified(listsOf(doubles()),
                                                            l -> isSorted(l.stream().sorted().collect(Collectors.toList())),
-                                                           141);
+                                                           76);
     assertEquals(2, failure.getMinimalCounterexample().getExampleValue().size());
   }
 
@@ -77,13 +78,13 @@ public class GeneratorTest extends PropertyCheckerTestCase {
   public void testStringOfStringChecksAllChars() {
     checkFalsified(stringsOf("abc "),
                    s -> !s.contains(" "),
-                   3);
+                   4);
   }
 
   public void testLongListsHappen() {
     PropertyFailure<List<Integer>> failure = checkFalsified(listsOf(integers()),
                                                             l -> l.size() < 200,
-                                                            631);
+                                                            504);
     assertEquals(200, failure.getMinimalCounterexample().getExampleValue().size());
   }
 
@@ -114,15 +115,31 @@ public class GeneratorTest extends PropertyCheckerTestCase {
   public void testBoolean() {
     PropertyFailure<List<Boolean>> failure = checkFalsified(listsOf(booleans()),
                                                             l -> !l.contains(true) || !l.contains(false),
-                                                            4);
+                                                            3);
     assertEquals(2, failure.getMinimalCounterexample().getExampleValue().size());
   }
 
   public void testShrinkingNonEmptyList() {
     PropertyFailure<List<Integer>> failure = checkFalsified(nonEmptyLists(integers(0, 100)),
                                                             l -> !l.contains(42),
-                                                            10);
+                                                            4);
     assertEquals(1, failure.getMinimalCounterexample().getExampleValue().size());
   }
 
+  public void testRecheckWithGivenSeeds() {
+    Generator<List<Integer>> gen = nonEmptyLists(integers(0, 100));
+    Predicate<List<Integer>> property = l -> !l.contains(42);
+
+    PropertyFailure<?> failure = checkFails(PropertyChecker.forAll(gen), property).getFailure();
+    assertTrue(failure.getIterationNumber() > 1);
+
+    PropertyFalsified e;
+
+    e = checkFails(PropertyChecker.forAll(gen).rechecking(failure.getIterationSeed(), failure.getSizeHint()), property);
+    assertEquals(1, e.getFailure().getIterationNumber());
+
+    e = checkFails(PropertyChecker.forAll(gen).withSeed(failure.getGlobalSeed()), property);
+    assertEquals(failure.getIterationNumber(), e.getFailure().getIterationNumber());
+  }
+
 }
diff --git a/slowCheck/test/slowCheck/PropertyCheckerTestCase.java b/slowCheck/test/slowCheck/PropertyCheckerTestCase.java
index c8b818c35ca3..cf791df7dd42 100644
--- a/slowCheck/test/slowCheck/PropertyCheckerTestCase.java
+++ b/slowCheck/test/slowCheck/PropertyCheckerTestCase.java
@@ -9,25 +9,30 @@ import java.util.function.Predicate;
  */
 abstract class PropertyCheckerTestCase extends TestCase {
 
-  protected  <T> PropertyFailure<T> checkFalsified(Generator<T> generator, Predicate<T> predicate, int minimizationSteps) {
+  protected <T> PropertyFalsified checkFails(PropertyChecker<T> checker, Predicate<T> predicate) {
     try {
-      forAllStable(generator).shouldHold(predicate);
+      checker.shouldHold(predicate);
       throw new AssertionError("Can't falsify " + getName());
     }
     catch (PropertyFalsified e) {
-      //noinspection unchecked
-      PropertyFailure<T> failure = (PropertyFailure<T>)e.getFailure();
-
-      System.out.println(" " + getName());
-      System.out.println("Value: " + e.getBreakingValue());
-      System.out.println("Data: " + e.getData());
-      assertEquals(minimizationSteps, failure.getTotalMinimizationExampleCount());
-      assertEquals(e.getBreakingValue(), generator.getGeneratorFunction().apply(e.getData()));
-
-      return failure;
+      return e;
     }
   }
 
+  protected <T> PropertyFailure<T> checkFalsified(Generator<T> generator, Predicate<T> predicate, int minimizationSteps) {
+    PropertyFalsified e = checkFails(forAllStable(generator), predicate);
+    //noinspection unchecked
+    PropertyFailure<T> failure = (PropertyFailure<T>)e.getFailure();
+
+    System.out.println(" " + getName());
+    System.out.println("Value: " + e.getBreakingValue());
+    System.out.println("Data: " + e.getData());
+    assertEquals(minimizationSteps, failure.getTotalMinimizationExampleCount());
+    assertEquals(e.getBreakingValue(), generator.getGeneratorFunction().apply(e.getData()));
+
+    return failure;
+  }
+
   protected static <T> PropertyChecker<T> forAllStable(Generator<T> generator) {
     return PropertyChecker.forAll(generator).withSeed(0);
   }