diff --git a/jedi/evaluate/precedence.py b/jedi/evaluate/precedence.py
index 22527c30..ee92c21a 100644
--- a/jedi/evaluate/precedence.py
+++ b/jedi/evaluate/precedence.py
@@ -16,9 +16,10 @@ class PythonGrammar(object):
         def __new__(cls, first, second):
             self = str.__new__(cls, first)
             self.second = second
+            return self
 
         def __str__(self):
-            return self.__str__() + ' ' + self.second
+            return str.__str__(self) + ' ' + self.second
 
     FACTOR = '+', '-', '~'
     POWER = '**',
@@ -31,7 +32,7 @@ class PythonGrammar(object):
     EXPR = '|',
 
     COMPARISON = ('<', '>', '==', '>=', '<=', '!=', 'in',
-                  MultiPart('not', 'in'), MultiPart('is', 'not')), 'is'
+                  MultiPart('not', 'in'), MultiPart('is', 'not'), 'is')
 
     NOT_TEST = 'not',
     AND_TEST = 'and',
@@ -58,7 +59,7 @@ class Precedence(object):
     def parse_tree(self, strip_literals=False):
         def process(which):
             try:
-                which = which.parse_tree()
+                which = which.parse_tree(strip_literals)
             except AttributeError:
                 pass
             if strip_literals and isinstance(which, pr.Literal):
@@ -124,7 +125,10 @@ def _check_operator(iterator, priority=PythonGrammar.LOWEST_PRIORITY):
                 next_tok = next(iterator)
                 if next_tok != match.second:
                     iterator.push_back(next_tok)
-                continue
+                    if el == 'is':  # `is not` special case
+                        match = 'is'
+                    else:
+                        continue
 
             operator = match
             break
@@ -132,7 +136,8 @@ def _check_operator(iterator, priority=PythonGrammar.LOWEST_PRIORITY):
         if operator is None:
             _syntax_error(el)
             continue
+
         right = _check_operator(iterator, check_prio)
         if right is not None:
-            left = Precedence(left, operator, right)
+            left = Precedence(left, str(operator), right)
     return left
diff --git a/test/test_evaluate/test_precedence.py b/test/test_evaluate/test_precedence.py
index 65c3e1a4..9d7630ee 100644
--- a/test/test_evaluate/test_precedence.py
+++ b/test/test_evaluate/test_precedence.py
@@ -21,9 +21,25 @@ def test_simple():
     assert parse_tree('+2') == (None, '+', 2)
 
 
+def test_prefixed():
+    assert parse_tree('--2') == (None, '-', (None, '-', 2))
+    assert parse_tree('1 and not - 2') == (1, 'and', (None, '-', 2))
+
+
 def test_invalid():
     """Should just return a simple operation."""
     assert parse_tree('1 +') == 1
     assert parse_tree('+') is None
 
     assert parse_tree('* 1') == 1
+    assert parse_tree('1 * * 1') == (1, '*', 1)
+
+    # invalid operator
+    assert parse_tree('1 not - 1') == (1, '-', 1)
+    assert parse_tree('1 - not ~1') == (1, '-', (None, '~', 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)