diff --git a/python/src/com/jetbrains/python/psi/types/PyTypeChecker.java b/python/src/com/jetbrains/python/psi/types/PyTypeChecker.java
index 95f8408722ba..f687a0147188 100644
--- a/python/src/com/jetbrains/python/psi/types/PyTypeChecker.java
+++ b/python/src/com/jetbrains/python/psi/types/PyTypeChecker.java
@@ -3,6 +3,8 @@ package com.jetbrains.python.psi.types;
 import com.jetbrains.python.psi.PyClass;
 import org.jetbrains.annotations.Nullable;
 
+import java.util.List;
+
 /**
  * @author vlan
  */
@@ -22,8 +24,14 @@ public class PyTypeChecker {
       return match(expected, ((PyTypeReference)actual).resolve(null, context), context);
     }
     if (actual instanceof PyUnionType) {
-      for (PyType t : ((PyUnionType)actual).getMembers()) {
-        if (!match(expected, t, context)) {
+      final List<PyType> members = ((PyUnionType)actual).getMembers();
+      for (PyType m : members) {
+        if (m == null) {
+          return true;
+        }
+      }
+      for (PyType m : members) {
+        if (!match(expected, m, context)) {
           return false;
         }
       }
diff --git a/python/src/com/jetbrains/python/psi/types/PyTypeParser.java b/python/src/com/jetbrains/python/psi/types/PyTypeParser.java
index d541496f1cc6..83fd47d9c3de 100644
--- a/python/src/com/jetbrains/python/psi/types/PyTypeParser.java
+++ b/python/src/com/jetbrains/python/psi/types/PyTypeParser.java
@@ -237,9 +237,7 @@ public class PyTypeParser {
     PyType result = null;
     for (TextRange range : ranges) {
       final PyType t = parse(anchor, range.substring(type), types, fullRanges, offset + range.getStartOffset());
-      if (t != null) {
-        result = (result == null) ? t : PyUnionType.union(result, t);
-      }
+      result = (result == null) ? t : PyUnionType.union(result, t);
     }
     return result;
   }
diff --git a/python/src/com/jetbrains/python/refactoring/PyDefUseUtil.java b/python/src/com/jetbrains/python/refactoring/PyDefUseUtil.java
index 6ebdfb0c79be..e2539f44c9d6 100644
--- a/python/src/com/jetbrains/python/refactoring/PyDefUseUtil.java
+++ b/python/src/com/jetbrains/python/refactoring/PyDefUseUtil.java
@@ -33,21 +33,9 @@ public class PyDefUseUtil {
       throw new InstructionNotFoundException();
     }
     final boolean[] visited = new boolean[instructions.length];
-    final Collection<PyElement> result = new HashSet<PyElement>();
+    final Collection<PyElement> result = new LinkedHashSet<PyElement>();
     getLatestDefs(var, instructions, instr, visited, result);
-    final List<PyElement> sortedResult = new ArrayList<PyElement>();
-    sortedResult.addAll(result);
-    Collections.sort(sortedResult, new Comparator<PyElement>() {
-      @Override
-      public int compare(PyElement e1, PyElement e2) {
-        final String n1 = e1.getName();
-        if (n1 != null) {
-          return n1.compareTo(e2.getName());
-        }
-        return 0;
-      }
-    });
-    return sortedResult.toArray(new PyElement[sortedResult.size()]);
+    return result.toArray(new PyElement[result.size()]);
   }
 
   private static void getLatestDefs(final PyElement var,
diff --git a/python/testData/inspections/PyTypeCheckerInspection/test.py b/python/testData/inspections/PyTypeCheckerInspection/test.py
index e1111cb9740c..b49e4b8cc137 100644
--- a/python/testData/inspections/PyTypeCheckerInspection/test.py
+++ b/python/testData/inspections/PyTypeCheckerInspection/test.py
@@ -220,4 +220,65 @@ def test_old_style_classes():
         :type x: object
         """
         pass
-    f(C()) #pass
\ No newline at end of file
+    f(C()) #pass
+
+
+def test_partly_unknown_type():
+    def f():
+        """
+        :rtype: None or unknown or int or long
+        """
+    def g(x):
+        """
+        :type x: object
+        """
+    g(f())
+
+
+def test_type_assertions():
+    def f_1():
+        """
+        :rtype: int or str or None
+        """
+    def f_2():
+        """
+        :rtype: int or None
+        """
+    def f_3():
+        """
+        :rtype: unknown
+        """
+    def f_4():
+        """
+        :rtype: object
+        """
+    def f_5():
+        """
+        :rtype: int or object
+        """
+    def f_6():
+        """
+        :rtype: int or unknown or float
+        """
+    def f_7():
+        """
+        :rtype: int or unknown
+        """
+    def print_int(x):
+        """
+        :type x: int
+        """
+        print(x)
+    def print_int_or_str(x):
+        """
+        :type x: int or str
+        """
+    x_1 = f_1()
+    print_int(<warning descr="Expected type 'int', got 'one of (int, str, None)' instead">x_1</warning>)
+    print_int_or_str(<warning descr="Expected type 'one of (int, str)', got 'one of (int, str, None)' instead">x_1</warning>)
+    if isinstance(x_1, int):
+        print_int(x_1)
+    if isinstance(x_1, str):
+        print_int_or_str(x_1)
+    x_7 = f_7()
+    print_int(x_7)
\ No newline at end of file
diff --git a/python/testData/quickdoc/Variable.html b/python/testData/quickdoc/Variable.html
new file mode 100644
index 000000000000..3b9fee740875
--- /dev/null
+++ b/python/testData/quickdoc/Variable.html
@@ -0,0 +1 @@
+<html><body><small>Assigned to <code>y</code><br></small><code><br>Inferred&nbsp;type:&nbsp;one&nbsp;of&nbsp;(str,&nbsp;int)</code></body></html>
\ No newline at end of file
diff --git a/python/testData/quickdoc/Variable.py b/python/testData/quickdoc/Variable.py
new file mode 100644
index 000000000000..9fdac0d1b811
--- /dev/null
+++ b/python/testData/quickdoc/Variable.py
@@ -0,0 +1,6 @@
+def f(x):
+    if x:
+        y = 1
+    else:
+        y = 'foo'
+    return <the_ref>y
\ No newline at end of file