diff --git a/jedi/api/__init__.py b/jedi/api/__init__.py
index 01ed0a34..5811cc8f 100644
--- a/jedi/api/__init__.py
+++ b/jedi/api/__init__.py
@@ -288,7 +288,7 @@ class Script(object):
 
     @memoize_default()
     def _get_under_cursor_stmt(self, cursor_txt):
-        tokenizer = source_tokens(cursor_txt, line_offset=self._pos[0] - 1)
+        tokenizer = source_tokens(cursor_txt)
         r = Parser(self._grammar, cursor_txt, tokenizer=tokenizer)
         try:
             # Take the last statement available.
@@ -304,7 +304,7 @@ class Script(object):
         else:
             pos = user_stmt.start_pos
 
-        stmt.move(0, pos[1])
+        stmt.move(pos[0] - 1, pos[1])  # Moving the offset.
         stmt.parent = self._parser.user_scope()
         return stmt
 
diff --git a/jedi/parser/fast.py b/jedi/parser/fast.py
index 9f48b50b..582f19ce 100644
--- a/jedi/parser/fast.py
+++ b/jedi/parser/fast.py
@@ -391,7 +391,7 @@ class FastParser(use_metaclass(CachedFastParser)):
                 nodes.remove(node)
                 break
         else:
-            tokenizer = FastTokenizer(parser_code, 0)
+            tokenizer = FastTokenizer(parser_code)
             self.number_parsers_used += 1
             #print('CODE', repr(source))
             p = Parser(self._grammar, parser_code, self.module_path, tokenizer=tokenizer)
@@ -410,10 +410,9 @@ class FastTokenizer(object):
     """
     Breaks when certain conditions are met, i.e. a new function or class opens.
     """
-    def __init__(self, source, line_offset=0):
-        # TODO remove the whole line_offset stuff, it's not used anymore.
+    def __init__(self, source):
         self.source = source
-        self._gen = source_tokens(source, line_offset)
+        self._gen = source_tokens(source)
         self._closed = False
 
         # fast parser options
diff --git a/jedi/parser/tokenize.py b/jedi/parser/tokenize.py
index 651f32b5..d70c2784 100644
--- a/jedi/parser/tokenize.py
+++ b/jedi/parser/tokenize.py
@@ -139,14 +139,14 @@ ALWAYS_BREAK_TOKEN = (';', 'import', 'from', 'class', 'def', 'try', 'except',
                       'finally', 'while', 'return')
 
 
-def source_tokens(source, line_offset=0):
+def source_tokens(source):
     """Generate tokens from a the source code (string)."""
     source = source + '\n'  # end with \n, because the parser needs it
     readline = StringIO(source).readline
-    return generate_tokens(readline, line_offset)
+    return generate_tokens(readline)
 
 
-def generate_tokens(readline, line_offset=0):
+def generate_tokens(readline):
     """
     A heavily modified Python standard library tokenizer.
 
@@ -156,7 +156,7 @@ def generate_tokens(readline, line_offset=0):
     """
     paren_level = 0  # count parentheses
     indents = [0]
-    lnum = line_offset
+    lnum = 0
     numchars = '0123456789'
     contstr = ''
     contline = None