diff --git a/jedi/api/interpreter.py b/jedi/api/interpreter.py
index 17540d6c..534447f5 100644
--- a/jedi/api/interpreter.py
+++ b/jedi/api/interpreter.py
@@ -99,7 +99,8 @@ class LazyName(helpers.FakeName):
             found = [evaluated]
 
         content = iterable.AlreadyEvaluated(found)
-        stmt = pt.ExprStmt([self, pt.Operator('=', (0, 0), ''), content])
+        stmt = pt.ExprStmt([self, pt.Operator(pt.zero_position_modifier,
+                                              '=', (0, 0), ''), content])
         stmt.parent = self._module
         return stmt
 
diff --git a/jedi/evaluate/compiled/fake.py b/jedi/evaluate/compiled/fake.py
index 954a5808..56d98d95 100644
--- a/jedi/evaluate/compiled/fake.py
+++ b/jedi/evaluate/compiled/fake.py
@@ -106,7 +106,7 @@ def get_faked(module, obj, name=None):
         # contain it).
         doc = '"""%s"""' % obj.__doc__  # TODO need escapes.
         suite = result.children[-1]
-        expr_stmt = pt.ExprStmt([pt.String(doc, (0, 0), '')])
+        expr_stmt = pt.ExprStmt([pt.String(pt.zero_position_modifier, doc, (0, 0), '')])
         new_line = pt.Whitespace('\n', (0, 0), '')
         docstr_node = pt.Node('simple_stmt', [expr_stmt, new_line])
         suite.children.insert(2, docstr_node)
diff --git a/jedi/evaluate/helpers.py b/jedi/evaluate/helpers.py
index 59bad818..ca94016d 100644
--- a/jedi/evaluate/helpers.py
+++ b/jedi/evaluate/helpers.py
@@ -158,8 +158,6 @@ def get_module_names(module, all_scopes):
 
 class FakeSubModule():
     line_offset = 0
-    parent = None
-    path = None
 
 
 class FakeImport(pr.Import):
@@ -196,7 +194,7 @@ class FakeName(pr.Name):
         In case is_definition is defined (not None), that bool value will be
         returned.
         """
-        super(FakeName, self).__init__(name_str, start_pos)
+        super(FakeName, self).__init__(pr.zero_position_modifier, name_str, start_pos)
         self.parent = parent
         self._is_definition = is_definition
 
diff --git a/jedi/evaluate/representation.py b/jedi/evaluate/representation.py
index 8b921ab5..9463020c 100644
--- a/jedi/evaluate/representation.py
+++ b/jedi/evaluate/representation.py
@@ -260,7 +260,9 @@ class LazyInstanceDict(object):
 
 class InstanceName(pr.Name):
     def __init__(self, origin_name, parent):
-        super(InstanceName, self).__init__(origin_name.value, origin_name.start_pos)
+        super(InstanceName, self).__init__(origin_name.position_modifier,
+                                           origin_name.value,
+                                           origin_name.start_pos)
         self._origin_name = origin_name
         self.parent = parent
 
diff --git a/jedi/parser/__init__.py b/jedi/parser/__init__.py
index dfd9fcbb..273cd96f 100644
--- a/jedi/parser/__init__.py
+++ b/jedi/parser/__init__.py
@@ -128,6 +128,8 @@ class Parser(object):
         self.used_names = {}
         self.scope_names_stack = [{}]
         self.error_statement_stacks = []
+        # For fast parser
+        self.position_modifier = pt.PositionModifier()
         p = PgenParser(grammar, self.convert_node, self.convert_leaf,
                        self.error_recovery)
         tokenizer = tokenizer or tokenize.source_tokens(source)
@@ -184,9 +186,9 @@ class Parser(object):
                 if value in ('def', 'class', 'lambda'):
                     self.scope_names_stack.append({})
 
-                return pt.Keyword(value, start_pos, prefix)
+                return pt.Keyword(self.position_modifier, value, start_pos, prefix)
             else:
-                name = pt.Name(value, start_pos, prefix)
+                name = pt.Name(self.position_modifier, value, start_pos, prefix)
                 # Keep a listing of all used names
                 arr = self.used_names.setdefault(name.value, [])
                 arr.append(name)
@@ -194,13 +196,13 @@ class Parser(object):
                 arr.append(name)
                 return name
         elif type == token.STRING:
-            return pt.String(value, start_pos, prefix)
+            return pt.String(self.position_modifier, value, start_pos, prefix)
         elif type == token.NUMBER:
-            return pt.Number(value, start_pos, prefix)
+            return pt.Number(self.position_modifier, value, start_pos, prefix)
         elif type in (token.NEWLINE, token.ENDMARKER):
-            return pt.Whitespace(value, start_pos, prefix)
+            return pt.Whitespace(self.position_modifier, value, start_pos, prefix)
         else:
-            return pt.Operator(value, start_pos, prefix)
+            return pt.Operator(self.position_modifier, value, start_pos, prefix)
 
     def error_recovery(self, grammar, stack, typ, value, start_pos, prefix,
                        add_token_callback):
diff --git a/jedi/parser/tree.py b/jedi/parser/tree.py
index 82a500de..34edb95d 100644
--- a/jedi/parser/tree.py
+++ b/jedi/parser/tree.py
@@ -51,6 +51,15 @@ def is_node(node, *symbol_names):
         return type in symbol_names
 
 
+class PositionModifier(object):
+    """A start_pos modifier for the fast parser."""
+    def __init__(self):
+        self.line = 0
+
+
+zero_position_modifier = PositionModifier()
+
+
 class DocstringMixin(object):
     __slots__ = ()
 
@@ -137,9 +146,10 @@ class Base(object):
 
 
 class Leaf(Base):
-    __slots__ = ('value', 'parent', 'start_pos', 'prefix')
+    __slots__ = ('position_modifier', 'value', 'parent', 'start_pos', 'prefix')
 
-    def __init__(self, value, start_pos, prefix=''):
+    def __init__(self, position_modifier, value, start_pos, prefix=''):
+        self.position_modifier = position_modifier
         self.value = value
         self.start_pos = start_pos
         self.prefix = prefix
@@ -620,7 +630,7 @@ class SubModule(Scope, Module):
             string = re.sub('\.[a-z]+-\d{2}[mud]{0,3}$', '', r.group(1))
         # Positions are not real, but a module starts at (1, 0)
         p = (1, 0)
-        name = Name(string, p)
+        name = Name(zero_position_modifier, string, p)
         name.parent = self
         return name