diff --git a/jedi/inference/syntax_tree.py b/jedi/inference/syntax_tree.py
index 8a0b2656..7983bef3 100644
--- a/jedi/inference/syntax_tree.py
+++ b/jedi/inference/syntax_tree.py
@@ -603,7 +603,11 @@ def _infer_comparison_part(inference_state, context, left, operator, right):
             if str_operator in ('is', '!=', '==', 'is not'):
                 operation = COMPARISON_OPERATORS[str_operator]
                 bool_ = operation(left, right)
-                return ValueSet([_bool_to_value(inference_state, bool_)])
+                # Only if == returns True or != returns False, we can continue.
+                # There's no guarantee that they are not equal. This can help
+                # in some cases, but does not cover everything.
+                if (str_operator in ('is', '==')) == bool_:
+                    return ValueSet([_bool_to_value(inference_state, bool_)])
 
             if isinstance(left, VersionInfo):
                 version_info = _get_tuple_ints(right)
diff --git a/test/completion/flow_analysis.py b/test/completion/flow_analysis.py
index 3eb50d5e..ed1f0533 100644
--- a/test/completion/flow_analysis.py
+++ b/test/completion/flow_analysis.py
@@ -75,6 +75,14 @@ def try_except(x):
 #? float() str()
 try_except(1)
 
+def test_function():
+    a = int(input())
+    if a % 2 == 0:
+        return True
+    return "False"
+
+#? bool() str()
+test_function()
 
 # -----------------
 # elif
@@ -145,7 +153,7 @@ elif 1 == True:
 a
 if check != 1:
     a = ''
-#? str()
+#? int() str()
 a
 if check == check:
     a = list
diff --git a/test/static_analysis/branches.py b/test/static_analysis/branches.py
index 458d854b..14ea9a7b 100644
--- a/test/static_analysis/branches.py
+++ b/test/static_analysis/branches.py
@@ -43,6 +43,9 @@ else:
 
 def addition(a, b):
     if type(a) == type(b):
+        # Might still be a type error, we might want to change this in the
+        # future.
+        #! 9 type-error-operation
         return a + b
     else:
         #! 9 type-error-operation
diff --git a/test/test_inference/test_compiled.py b/test/test_inference/test_compiled.py
index cab6e27c..92111b2a 100644
--- a/test/test_inference/test_compiled.py
+++ b/test/test_inference/test_compiled.py
@@ -174,10 +174,11 @@ def test_qualified_names(same_process_inference_state, obj, expected_names):
 
 def test_operation(Script, inference_state, create_compiled_object):
     b = create_compiled_object(bool)
-    true, = _infer_comparison_part(
+    false, true = _infer_comparison_part(
         inference_state, b.parent_context,
         left=list(b.execute_with_values())[0],
         operator=u'is not',
         right=b,
     )
+    assert false.py__name__() == 'bool'
     assert true.py__name__() == 'bool'