diff --git a/jedi/parser/__init__.py b/jedi/parser/__init__.py
index 74222628..c2743220 100644
--- a/jedi/parser/__init__.py
+++ b/jedi/parser/__init__.py
@@ -200,7 +200,8 @@ class Parser(object):
         else:
             return pt.Operator(value, start_pos, prefix)
 
-    def error_recovery(self, grammar, stack, typ, value, start_pos):
+    def error_recovery(self, grammar, stack, typ, value, start_pos, prefix,
+                       add_token_callback):
         """
         This parser is written in a dynamic way, meaning that this parser
         allows using different grammars (even non-Python). However, error
@@ -208,7 +209,7 @@ class Parser(object):
         """
         # For now just discard everything that is not a suite or
         # file_input, if we detect an error.
-        for index, (dfa, state, (_type, _)) in reversed(list(enumerate(stack))):
+        for index, (dfa, state, (_type, nodes)) in reversed(list(enumerate(stack))):
             # `suite` can sometimes be only simple_stmt, not stmt.
             symbol = grammar.number2symbol[_type]
             if symbol in ('file_input', 'suite'):
@@ -216,7 +217,17 @@ class Parser(object):
         # No success finding a transition
         print('err', tokenize.tok_name[typ], repr(value), start_pos, len(stack), index)
         self._stack_removal(grammar, stack, index + 1, value, start_pos)
-        return value not in ('def', 'class')
+        # Those can always be new statements.
+        if value in ('import', 'from', 'class', 'def', 'try', 'while', 'return'):
+            pass
+        elif typ == tokenize.DEDENT:
+            if symbol == 'suite':
+                if len(nodes) > 2:
+                    add_token_callback(typ, value, prefix, start_pos)
+                else:
+                    # If a function or anything else contains a suite that is
+                    # "empty" (just NEWLINE/INDENT), we remove it.
+                    self._stack_removal(grammar, stack, len(stack) - 2, value, start_pos)
 
     def _stack_removal(self, grammar, stack, start_index, value, start_pos):
         def clear_names(children):
diff --git a/jedi/parser/pgen2/parse.py b/jedi/parser/pgen2/parse.py
index f530d57c..08538937 100644
--- a/jedi/parser/pgen2/parse.py
+++ b/jedi/parser/pgen2/parse.py
@@ -104,6 +104,7 @@ class Parser(object):
         the parser stack we are able to do error recovery from wrong indents.
         """
         for type, value, prefix, start_pos in tokenizer:
+            #print(token.tok_name[type], value)
             yield type, value, prefix, start_pos
 
     def parse(self, tokenizer):
@@ -111,9 +112,12 @@ class Parser(object):
             if self.addtoken(type, value, prefix, start_pos):
                 break
         else:
-            # We never broke out -- EOF is too soon (how can this happen???)
-            # Hint: It probably doesn't since there's an ENDMARKER.
-            raise ParseError("incomplete input", type, value, start_pos)
+            # We never broke out -- EOF is too soon -- Unfinished statement.
+            self.error_recovery(self.grammar, self.stack, type, value,
+                                start_pos, prefix, self.addtoken)
+            # Add the ENDMARKER again.
+            if not self.addtoken(type, value, prefix, start_pos):
+                raise ParseError("incomplete input", type, value, start_pos)
         return self.rootnode
 
     def addtoken(self, type, value, prefix, start_pos):
@@ -166,9 +170,9 @@ class Parser(object):
                         # Done parsing, but another token is input
                         raise ParseError("too much input", type, value, start_pos)
                 else:
-                    if self.error_recovery(self.grammar, self.stack, type,
-                                           value, start_pos):
-                        break
+                    self.error_recovery(self.grammar, self.stack, type,
+                                        value, start_pos, prefix, self.addtoken)
+                    break
 
     def classify(self, type, value, start_pos):
         """Turn a token into a label.  (Internal)"""
diff --git a/jedi/parser/tokenize.py b/jedi/parser/tokenize.py
index abbf62a3..010eb890 100644
--- a/jedi/parser/tokenize.py
+++ b/jedi/parser/tokenize.py
@@ -320,9 +320,16 @@ def generate_tokens(readline, line_offset=0):
                 else:                                       # ordinary string
                     yield Token(STRING, token, spos, prefix)
             elif initial in namechars:                      # ordinary name
-                yield Token(NAME, token, spos, prefix)
                 if token in ALWAYS_BREAK_TOKEN:
                     paren_level = 0
+                    while True:
+                        indent = indents.pop()
+                        if indent > start:
+                            yield Token(DEDENT, '', (lnum, 0), '')
+                        else:
+                            indents.append(indent)
+                            break
+                yield Token(NAME, token, spos, prefix)
             elif initial == '\\' and line[start:] == '\\\n':  # continued stmt
                 continue
             else: