diff --git a/flask/cli.py b/flask/cli.py
index 3440d981..a812ae2e 100644
--- a/flask/cli.py
+++ b/flask/cli.py
@@ -77,6 +77,8 @@ def find_best_app(script_info, module):
                 if isinstance(app, Flask):
                     return app
             except TypeError:
+                if not _called_with_wrong_args(app_factory):
+                    raise
                 raise NoAppException(
                     'Detected factory "{factory}" in module "{module}", but '
                     'could not call it without arguments. Use '
@@ -113,6 +115,30 @@ def call_factory(script_info, app_factory, arguments=()):
     return app_factory()
 
 
+def _called_with_wrong_args(factory):
+    """Check whether calling a function raised a ``TypeError`` because
+    the call failed or because something in the factory raised the
+    error.
+
+    :param factory: the factory function that was called
+    :return: true if the call failed
+    """
+    tb = sys.exc_info()[2]
+
+    try:
+        while tb is not None:
+            if tb.tb_frame.f_code is factory.__code__:
+                # in the factory, it was called successfully
+                return False
+
+            tb = tb.tb_next
+
+        # didn't reach the factory
+        return True
+    finally:
+        del tb
+
+
 def find_app_by_string(script_info, module, app_name):
     """Checks if the given string is a variable name or a function. If it is a
     function, it checks for specified arguments and whether it takes a
@@ -150,6 +176,9 @@ def find_app_by_string(script_info, module, app_name):
         try:
             app = call_factory(script_info, attr, args)
         except TypeError as e:
+            if not _called_with_wrong_args(attr):
+                raise
+
             raise NoAppException(
                 '{e}\nThe factory "{app_name}" in module "{module}" could not '
                 'be called with the specified arguments.'.format(
diff --git a/tests/test_cli.py b/tests/test_cli.py
index f1e5eba7..3ffb3034 100644
--- a/tests/test_cli.py
+++ b/tests/test_cli.py
@@ -135,6 +135,13 @@ def test_find_best_app(test_apps):
 
     pytest.raises(NoAppException, find_best_app, script_info, Module)
 
+    class Module:
+        @staticmethod
+        def create_app():
+            raise TypeError('bad bad factory!')
+
+    pytest.raises(TypeError, find_best_app, script_info, Module)
+
 
 @pytest.mark.parametrize('value,path,result', (
     ('test', cwd, 'test'),