diff --git a/jedi/evaluate/compiled/__init__.py b/jedi/evaluate/compiled/__init__.py
index ee18d5d4..b676406e 100644
--- a/jedi/evaluate/compiled/__init__.py
+++ b/jedi/evaluate/compiled/__init__.py
@@ -412,6 +412,9 @@ magic_function_class = CompiledObject(type(load_module), parent=builtin)
 generator_obj = CompiledObject(_a_generator(1.0))
 type_names = []  # Need this, because it's return in get_defined_names.
 type_names = builtin.get_by_name('type').get_defined_names()
+none_obj = builtin.get_by_name('None')
+false_obj = builtin.get_by_name('False')
+true_obj = builtin.get_by_name('True')
 
 
 def compiled_objects_cache(func):
diff --git a/jedi/evaluate/precedence.py b/jedi/evaluate/precedence.py
index 39e4afc9..8f453cae 100644
--- a/jedi/evaluate/precedence.py
+++ b/jedi/evaluate/precedence.py
@@ -1,14 +1,24 @@
 """
 Handles operator precedence.
 """
+import operator
 
 from jedi._compatibility import unicode
 from jedi.parser import representation as pr
 from jedi import debug
 from jedi.common import PushBackIterator
-from jedi.evaluate.compiled import CompiledObject, create, builtin
+from jedi.evaluate.compiled import (CompiledObject, create, builtin, false_obj,
+                                    true_obj, none_obj)
 from jedi.evaluate import analysis
 
+# Maps Python syntax to the operator module.
+OPERATOR_MAPPING = {
+    '==': operator.eq,
+    '!=': operator.ne,
+    'is': operator.is_,
+    'is not': operator.is_not,
+}
+
 
 class PythonGrammar(object):
     """
@@ -260,6 +270,15 @@ def _is_list(obj):
     return isinstance(obj, iterable.Array) and obj.type == pr.Array.LIST
 
 
+def _keyword_from_value(obj):
+    if obj is None:
+        return none_obj
+    elif obj is False:
+        return false_obj
+    elif obj is True:
+        return true_obj
+
+
 def _element_calculate(evaluator, left, operator, right):
     from jedi.evaluate import iterable, representation as er
     l_is_num = _is_number(left)
@@ -282,6 +301,13 @@ def _element_calculate(evaluator, left, operator, right):
         # With strings and numbers the left type typically remains. Except for
         # `int() % float()`.
         return [left]
+    elif operator in OPERATOR_MAPPING:
+        operation = OPERATOR_MAPPING[operator]
+        if isinstance(left, CompiledObject) and isinstance(right, CompiledObject):
+            # Possible, because the return is not an option. Just compare.
+            left = left.obj
+            right = right.obj
+        return [_keyword_from_value(operation(left, right))]
 
     def check(obj):
         """Checks if a Jedi object is either a float or an int."""
diff --git a/test/completion/flow_analysis.py b/test/completion/flow_analysis.py
index 2b0730fb..3cff6af0 100644
--- a/test/completion/flow_analysis.py
+++ b/test/completion/flow_analysis.py
@@ -88,12 +88,41 @@ def check(a):
     if a is None:
         return 1
     return ''
+    return set
 
 #? int()
 check(None)
 #? str()
 check('asb')
 
+a = list
+if 2 == True:
+    a = set
+elif 1 == True:
+    a = 0
+
+#? int()
+a
+if check != 1:
+    a = ''
+#? str()
+a
+if check == check:
+    a = list
+#? list
+a
+if check != check:
+    a = set
+else:
+    a = dict
+#? dict
+a
+if (check is not check):
+    a = 1
+#? dict
+a
+
+
 # -----------------
 # name resolution
 # -----------------
@@ -121,5 +150,3 @@ else:
 
 #? int
 a
-
-