diff --git a/jedi/evaluate/precedence.py b/jedi/evaluate/precedence.py
index ee92c21a..49a58db6 100644
--- a/jedi/evaluate/precedence.py
+++ b/jedi/evaluate/precedence.py
@@ -113,7 +113,9 @@ def _check_operator(iterator, priority=PythonGrammar.LOWEST_PRIORITY):
         operator = None
         for check_prio, check in enumerate(PythonGrammar.ORDER):
             if check_prio >= priority:
-                break  # respect priorities.
+                # respect priorities.
+                iterator.push_back(el)
+                return left
 
             try:
                 match_index = check.index(el)
@@ -137,6 +139,8 @@ def _check_operator(iterator, priority=PythonGrammar.LOWEST_PRIORITY):
             _syntax_error(el)
             continue
 
+        if operator == '**':
+            check_prio += 1  # to the power of is right-associative
         right = _check_operator(iterator, check_prio)
         if right is not None:
             left = Precedence(left, str(operator), right)
diff --git a/test/test_evaluate/test_precedence.py b/test/test_evaluate/test_precedence.py
index 9d7630ee..14aa3dea 100644
--- a/test/test_evaluate/test_precedence.py
+++ b/test/test_evaluate/test_precedence.py
@@ -19,6 +19,7 @@ def parse_tree(statement_string):
 def test_simple():
     assert parse_tree('1+2') == (1, '+', 2)
     assert parse_tree('+2') == (None, '+', 2)
+    assert parse_tree('1+2-3') == ((1, '+', 2), '-', 3)
 
 
 def test_prefixed():
@@ -38,8 +39,15 @@ def test_invalid():
     assert parse_tree('1 not - 1') == (1, '-', 1)
     assert parse_tree('1 - not ~1') == (1, '-', (None, '~', 1))
 
+    # not not allowed
+    assert parse_tree('1 is not not 1') == (1, 'is not', 1)
+
 
 def test_multi_part():
     assert parse_tree('1 not in 2') == (1, 'not in', 2)
     assert parse_tree('1 is not -1') == (1, 'is not', (None, '-', 1))
     assert parse_tree('1 is 1') == (1, 'is', 1)
+
+
+def test_power():
+    assert parse_tree('2 ** 3 ** 4') == (2, '**', (3, '**', 4))