diff --git a/docs/source/command_line.rst b/docs/source/command_line.rst
index 0ea5981c31d1..ad7555bb2759 100644
--- a/docs/source/command_line.rst
+++ b/docs/source/command_line.rst
@@ -274,6 +274,22 @@ Here are some more useful flags:
   re-check your code without ``--strict-optional`` to ensure new type errors
   are not introduced.
 
+.. _disallow-any:
+
+- ``--disallow-any`` disallows various types of ``Any`` in a module.
+  The option takes a comma-separated list of the following values:
+  ``unimported``, ``unannotated``.
+
+  ``unimported`` disallows usage of types that come from unfollowed imports
+  (such types become aliases for ``Any``). Unfollowed imports occur either
+  when the imported module does not exist or when ``--follow-imports=skip``
+  is set.
+
+  ``unannotated`` disallows function definitions that are not fully
+  typed (i.e. that are missing an explicit type annotation for any
+  of the parameters or the return type). ``unannotated`` option is
+  interchangeable with ``--disallow-untyped-defs``.
+
 - ``--disallow-untyped-defs`` reports an error whenever it encounters
   a function definition without type annotations.
 
diff --git a/docs/source/config_file.rst b/docs/source/config_file.rst
index 6fe139b1bb8c..07db822df8a1 100644
--- a/docs/source/config_file.rst
+++ b/docs/source/config_file.rst
@@ -147,6 +147,12 @@ overridden by the pattern sections matching the module name.
 - ``almost_silent`` (Boolean, deprecated) equivalent to
   ``follow_imports=skip``.
 
+- ``disallow_any`` (Comma-separated list, default empty) is an option to
+  disallow various types of ``Any`` in a module. The flag takes a
+  comma-separated list of the following arguments: ``unimported``,
+  ``unannotated``. For explanations see the discussion for the
+  :ref:`--disallow-any <disallow-any>` option.
+
 - ``disallow_untyped_calls`` (Boolean, default False) disallows
   calling functions without type annotations from functions with type
   annotations.
diff --git a/mypy/main.py b/mypy/main.py
index 422ca3ccec03..eb28b7e3bdb4 100644
--- a/mypy/main.py
+++ b/mypy/main.py
@@ -97,7 +97,7 @@ def type_check_only(sources: List[BuildSource], bin_dir: str, options: Options)
                        options=options)
 
 
-disallow_any_options = ['unimported']
+disallow_any_options = ['unimported', 'unannotated']
 
 
 def disallow_any_argument_type(raw_options: str) -> List[str]:
@@ -201,7 +201,6 @@ def process_options(args: List[str],
 
     strict_flag_names = []  # type: List[str]
     strict_flag_assignments = []  # type: List[Tuple[str, bool]]
-    disallow_any_options = ['unimported']
 
     def add_invertible_flag(flag: str,
                             *,
@@ -428,6 +427,9 @@ def add_invertible_flag(flag: str,
         print("Warning: --no-fast-parser no longer has any effect.  The fast parser "
               "is now mypy's default and only parser.")
 
+    if 'unannotated' in options.disallow_any:
+        options.disallow_untyped_defs = True
+
     # Check for invalid argument combinations.
     if require_targets:
         code_methods = sum(bool(c) for c in [special_opts.modules,
@@ -724,6 +726,8 @@ def parse_section(prefix: str, template: Options,
         except ValueError as err:
             print("%s: %s: %s" % (prefix, key, err), file=sys.stderr)
             continue
+        if key == 'disallow_any':
+            results['disallow_untyped_defs'] = v and 'unannotated' in v
         if key == 'silent_imports':
             print("%s: silent_imports has been replaced by "
                   "ignore_missing_imports=True; follow_imports=skip" % prefix, file=sys.stderr)
diff --git a/test-data/unit/check-flags.test b/test-data/unit/check-flags.test
index 6f8dcdd4a94b..6ee0247c9bf4 100644
--- a/test-data/unit/check-flags.test
+++ b/test-data/unit/check-flags.test
@@ -44,6 +44,12 @@ def f():
     1 + "str"
 [out]
 main:2: error: Function is missing a type annotation
+[case testUntypedDefDisallowUnannotated]
+# flags: --disallow-any=unannotated
+def f():
+    1 + "str"
+[out]
+main:2: error: Function is missing a type annotation
 
 [case testSubclassingAny]
 # flags: --disallow-subclassing-any
diff --git a/test-data/unit/cmdline.test b/test-data/unit/cmdline.test
index 118a7c0f5452..cfc50f819a36 100644
--- a/test-data/unit/cmdline.test
+++ b/test-data/unit/cmdline.test
@@ -176,6 +176,76 @@ z.py:1: error: Function is missing a type annotation
 z.py:4: error: Call to untyped function "f" in typed context
 x.py:1: error: Function is missing a type annotation
 
+[case testPerFileConfigSectionUntypedWithDisallowUnannotated]
+# cmd: mypy w.py x.py y.py z.py
+[file mypy.ini]
+[[mypy]
+disallow_any = unannotated
+[[mypy-y*]
+disallow_any =
+[[mypy-z*]
+disallow_untyped_defs = True
+[[mypy-w*]
+disallow_untyped_defs = False
+[file x.py]
+def f(a):
+    pass
+[file y.py]
+def f(a):
+    pass
+[file z.py]
+def f(a):
+    pass
+[file w.py]
+def f(a):
+    pass
+[out]
+z.py:1: error: Function is missing a type annotation
+x.py:1: error: Function is missing a type annotation
+
+[case testPerFileConfigSectionDisallowUnannotatedWithUntyped]
+# cmd: mypy x.py y.py z.py
+[file mypy.ini]
+[[mypy]
+disallow_untyped_defs = True
+[[mypy-y*]
+disallow_any =
+[[mypy-z*]
+disallow_any = unannotated
+[file x.py]
+def f(a):
+    pass
+[file y.py]
+def f(a):
+    pass
+[file z.py]
+def f(a):
+    pass
+[out]
+z.py:1: error: Function is missing a type annotation
+x.py:1: error: Function is missing a type annotation
+
+[case testPerFileConfigSectionDisallowUnannotatedNoOverride]
+# cmd: mypy x.py y.py z.py
+[file mypy.ini]
+[[mypy]
+[[mypy-x*]
+disallow_untyped_defs = True
+[[mypy-z*]
+disallow_any = unannotated
+[file x.py]
+def f(a):
+    pass
+[file y.py]
+def f(a):
+    pass
+[file z.py]
+def f(a):
+    pass
+[out]
+z.py:1: error: Function is missing a type annotation
+x.py:1: error: Function is missing a type annotation
+
 [case testPerFileConfigSectionMultipleMatches]
 # cmd: mypy xx.py xy.py yx.py yy.py
 [file mypy.ini]