diff --git a/mypy/newsemanal/semanal.py b/mypy/newsemanal/semanal.py
index b504d96b7919..505b1092ac2e 100644
--- a/mypy/newsemanal/semanal.py
+++ b/mypy/newsemanal/semanal.py
@@ -491,8 +491,15 @@ def file_context(self, file_node: MypyFile, fnam: str, options: Options,
         del self.options
 
     def visit_func_def(self, defn: FuncDef) -> None:
-        if not defn.is_decorated and not defn.is_overload:
-            self.add_func_to_symbol_table(defn)
+        defn.is_conditional = self.block_depth[-1] > 0
+
+        # We don't add module top-level functions to symbol tables
+        # when we analyze their bodies in the second phase on analysis,
+        # since they were added in the first phase. Nested functions
+        # get always added, since they aren't separate targets.
+        if not self.recurse_into_functions or len(self.function_stack) > 0:
+            if not defn.is_decorated and not defn.is_overload:
+                self.add_func_to_symbol_table(defn)
 
         if not self.recurse_into_functions:
             return
@@ -515,8 +522,6 @@ def _visit_func_def(self, defn: FuncDef) -> None:
             self.update_function_type_variables(defn.type, defn)
         self.function_stack.pop()
 
-        defn.is_conditional = self.block_depth[-1] > 0
-
         if self.is_class_scope():
             # Method definition
             assert self.type is not None
@@ -574,7 +579,7 @@ def prepare_method_signature(self, func: FuncDef, info: TypeInfo) -> None:
                         leading_type = self.class_type(leading_type)
                     func.type = replace_implicit_first_type(functype, leading_type)
 
-    def set_original_def(self, previous: Optional[Node], new: FuncDef) -> bool:
+    def set_original_def(self, previous: Optional[Node], new: Union[FuncDef, Decorator]) -> bool:
         """If 'new' conditionally redefine 'previous', set 'previous' as original
 
         We reject straight redefinitions of functions, as they are usually
@@ -583,6 +588,8 @@ def set_original_def(self, previous: Optional[Node], new: FuncDef) -> bool:
           def f(): ...
           def f(): ...  # Error: 'f' redefined
         """
+        if isinstance(new, Decorator):
+            new = new.func
         if isinstance(previous, (FuncDef, Var, Decorator)) and new.is_conditional:
             new.original_def = previous
             return True
@@ -2789,6 +2796,7 @@ def process_module_assignment(self, lvals: List[Lvalue], rval: Expression,
                             lnode.node = rnode.node
 
     def visit_decorator(self, dec: Decorator) -> None:
+        dec.func.is_conditional = self.block_depth[-1] > 0
         if not dec.is_overload:
             self.add_symbol(dec.name(), dec, dec)
         dec.func._fullname = self.qualified_name(dec.name())
@@ -3954,12 +3962,39 @@ def add_symbol_table_node(self, name: str, symbol: SymbolTableNode,
                 and context is not None
                 and not isinstance(existing.node, PlaceholderNode)):
             if existing.node != symbol.node:
-                self.name_already_defined(name, context, existing)
+                if isinstance(symbol.node, (FuncDef, Decorator)):
+                    self.add_func_redefinition(names, name, symbol)
+                if not (isinstance(symbol.node, (FuncDef, Decorator))
+                        and self.set_original_def(existing.node, symbol.node)):
+                    self.name_already_defined(name, context, existing)
         elif name not in self.missing_names and '*' not in self.missing_names:
             names[name] = symbol
             return True
         return False
 
+    def add_func_redefinition(self, names: SymbolTable, name: str,
+                              symbol: SymbolTableNode) -> None:
+        """Add a symbol table node that reflects a redefinition of a function.
+
+        Redefinitions need to be added to the symbol table so that they can be found
+        through AST traversal, but they have dummy names of form 'name-redefinition[N]',
+        where N ranges over 2, 3, ... (omitted for the first redefinition).
+        """
+        i = 1
+        while True:
+            if i == 1:
+                new_name = '{}-redefinition'.format(name)
+            else:
+                new_name = '{}-redefinition{}'.format(name, i)
+            existing = names.get(new_name)
+            if existing is None:
+                names[new_name] = symbol
+                return
+            elif existing.node is symbol.node:
+                # Already there
+                return
+            i += 1
+
     def add_module_symbol(self, id: str, as_id: str, module_public: bool,
                           context: Context, module_hidden: bool = False) -> None:
         """Add symbol that is a reference to a module object."""
diff --git a/mypy/newsemanal/semanal_main.py b/mypy/newsemanal/semanal_main.py
index ce8586651ce4..5244aca0a25f 100644
--- a/mypy/newsemanal/semanal_main.py
+++ b/mypy/newsemanal/semanal_main.py
@@ -160,7 +160,11 @@ def get_all_leaf_targets(symtable: SymbolTable,
     """Return all leaf targets in a symbol table (module-level and methods)."""
     result = []  # type: List[TargetInfo]
     for name, node in symtable.items():
-        new_prefix = prefix + '.' + name
+        shortname = name
+        if '-redef' in name:
+            # Restore original name from mangled name of multiply defined function
+            shortname = name.split('-redef')[0]
+        new_prefix = prefix + '.' + shortname
         if isinstance(node.node, (FuncDef, TypeInfo, OverloadedFuncDef, Decorator)):
             if node.node.fullname() == new_prefix:
                 if isinstance(node.node, TypeInfo):
diff --git a/test-data/unit/check-newsemanal.test b/test-data/unit/check-newsemanal.test
index ec108f9f0252..5368354c6647 100644
--- a/test-data/unit/check-newsemanal.test
+++ b/test-data/unit/check-newsemanal.test
@@ -1417,3 +1417,68 @@ reveal_type(x)  # E: Revealed type is 'Tuple[builtins.int, builtins.int]'
 [file b.py]
 import a
 x = (1, 2)
+
+[case testNewAnalyzerConditionalFunc]
+if int():
+    def f(x: int) -> None:
+        pass
+    def g(x: int) -> None:
+        pass
+elif bool():
+    def f(x: int) -> None:
+        1()  # E: "int" not callable
+    def g(x: str) -> None:  # E: All conditional function variants must have identical signatures
+        pass
+else:
+    def f(x: int) -> None:
+        ''()  # E: "str" not callable
+
+reveal_type(g) # E: Revealed type is 'def (x: builtins.int)'
+
+[case testNewAnalyzerConditionalFuncDefer]
+if int():
+    def f(x: A) -> None:
+        pass
+    def g(x: A) -> None:
+        pass
+else:
+    def f(x: A) -> None:
+        1()  # E: "int" not callable
+    def g(x: str) -> None:  # E: All conditional function variants must have identical signatures
+        pass
+
+reveal_type(g) # E: Revealed type is 'def (x: __main__.A)'
+
+class A: pass
+
+[case testNewAnalyzerConditionalDecoratedFunc]
+from typing import Callable
+
+def dec(f: Callable[[int], None]) -> Callable[[str], None]:
+    pass
+
+if int():
+    from m import f
+else:
+    @dec
+    def f(x: int) -> None:
+        1()  # E: "int" not callable
+reveal_type(f) # E: Revealed type is 'def (x: builtins.str)'
+[file m.py]
+def f(x: str) -> None: pass
+
+[case testNewAnalyzerConditionallyDefineFuncOverVar]
+from typing import Callable
+
+if int():
+    f: Callable[[str], None]
+else:
+    def f(x: str) -> None:
+        ...
+reveal_type(f) # E: Revealed type is 'def (builtins.str)'
+
+[case testNewAnalyzerConditionallyDefineFuncOverClass]
+class C:
+    1()  # E: "int" not callable
+def C() -> None:  # E: Name 'C' already defined on line 1
+    ''()  # E: "str" not callable