diff --git a/java/java-analysis-impl/src/com/intellij/codeInspection/dataFlow/DfaPsiUtil.java b/java/java-analysis-impl/src/com/intellij/codeInspection/dataFlow/DfaPsiUtil.java
index 76f3d1b92a61..bf0f3d10b17a 100644
--- a/java/java-analysis-impl/src/com/intellij/codeInspection/dataFlow/DfaPsiUtil.java
+++ b/java/java-analysis-impl/src/com/intellij/codeInspection/dataFlow/DfaPsiUtil.java
@@ -1,5 +1,5 @@
 /*
- * Copyright 2000-2015 JetBrains s.r.o.
+ * Copyright 2000-2016 JetBrains s.r.o.
  *
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
@@ -29,6 +29,7 @@ import com.intellij.psi.search.LocalSearchScope;
 import com.intellij.psi.search.searches.ReferencesSearch;
 import com.intellij.psi.tree.IElementType;
 import com.intellij.psi.util.*;
+import com.intellij.util.ArrayUtil;
 import com.intellij.util.NullableFunction;
 import com.intellij.util.containers.ContainerUtil;
 import com.intellij.util.containers.MultiMap;
@@ -102,6 +103,10 @@ public class DfaPsiUtil {
     if (PsiJavaPatterns.psiParameter().withParents(PsiParameterList.class, PsiLambdaExpression.class).accepts(owner)) {
       PsiLambdaExpression lambda = (PsiLambdaExpression)owner.getParent().getParent();
       int index = lambda.getParameterList().getParameterIndex((PsiParameter)owner);
+      Nullness nullness = inferLambdaParameterNullness(lambda, index);
+      if(nullness != Nullness.UNKNOWN) {
+        return nullness;
+      }
       PsiMethod sam = LambdaUtil.getFunctionalInterfaceMethod(lambda.getFunctionalInterfaceType());
       if (sam != null && index < sam.getParameterList().getParametersCount()) {
         return getElementNullability(null, sam.getParameterList().getParameters()[index]);
@@ -111,6 +116,43 @@ public class DfaPsiUtil {
     return Nullness.UNKNOWN;
   }
 
+  @NotNull
+  private static Nullness inferLambdaParameterNullness(PsiLambdaExpression lambda, int parameterIndex) {
+    PsiElement expression = lambda;
+    PsiElement expressionParent = lambda.getParent();
+    while(expressionParent instanceof PsiConditionalExpression) {
+      expression = expressionParent;
+      expressionParent = expressionParent.getParent();
+    }
+    if(expressionParent instanceof PsiExpressionList) {
+      PsiExpressionList list = (PsiExpressionList)expressionParent;
+      PsiElement listParent = list.getParent();
+      if(listParent instanceof PsiMethodCallExpression) {
+        PsiMethod method = ((PsiMethodCallExpression)listParent).resolveMethod();
+        if(method != null) {
+          int expressionIndex = ArrayUtil.find(list.getExpressions(), expression);
+          return getLambdaParameterNullness(method, expressionIndex, parameterIndex);
+        }
+      }
+    }
+    return Nullness.UNKNOWN;
+  }
+
+  @NotNull
+  private static Nullness getLambdaParameterNullness(@NotNull PsiMethod method, int parameterIndex, int lambdaParameterIndex) {
+    PsiClass type = method.getContainingClass();
+    if(type != null) {
+      if(CommonClassNames.JAVA_UTIL_OPTIONAL.equals(type.getQualifiedName())) {
+        String methodName = method.getName();
+        if((methodName.equals("map") || methodName.equals("filter") || methodName.equals("ifPresent") || methodName.equals("flatMap"))
+          && parameterIndex == 0 && lambdaParameterIndex == 0) {
+          return Nullness.NOT_NULL;
+        }
+      }
+    }
+    return Nullness.UNKNOWN;
+  }
+
   private static boolean isNotNullLocally(@NotNull PsiModifierListOwner owner) {
     NullableNotNullManager nnnm = NullableNotNullManager.getInstance(owner.getProject());
     PsiAnnotation notNullAnno = nnnm.getNotNullAnnotation(owner, true);
diff --git a/java/java-tests/testData/inspection/dataFlow/fixture/NotNullOptionalLambdaParameter.java b/java/java-tests/testData/inspection/dataFlow/fixture/NotNullOptionalLambdaParameter.java
new file mode 100644
index 000000000000..508861cfb9c3
--- /dev/null
+++ b/java/java-tests/testData/inspection/dataFlow/fixture/NotNullOptionalLambdaParameter.java
@@ -0,0 +1,10 @@
+import java.util.stream.Stream;
+
+class Example {
+  public static void main(String[] args) {
+    Stream.of(args).filter(arg -> arg.startsWith("a"))
+      .findFirst().ifPresent(args.length == 1 ? value -> {} : value -> {
+      System.out.println(<warning descr="Condition 'value == null' is always 'false'">value == null</warning> ? "none" : value);
+    });
+  }
+}
diff --git a/java/java-tests/testSrc/com/intellij/codeInspection/DataFlowInspection8Test.java b/java/java-tests/testSrc/com/intellij/codeInspection/DataFlowInspection8Test.java
index 0e766d54f1bd..1554016ddf7b 100644
--- a/java/java-tests/testSrc/com/intellij/codeInspection/DataFlowInspection8Test.java
+++ b/java/java-tests/testSrc/com/intellij/codeInspection/DataFlowInspection8Test.java
@@ -49,6 +49,7 @@ public class DataFlowInspection8Test extends DataFlowInspectionTestCase {
   public void testOptionalOfNullable() { doTest(); }
   public void testPrimitiveInVoidLambda() { doTest(); }
   public void testNotNullLambdaParameter() { doTest(); }
+  public void testNotNullOptionalLambdaParameter() { doTest(); }
 
   public void testNullArgumentIsFailingMethodCall() {
     doTest();