diff --git a/mypy/build.py b/mypy/build.py
index 59d46cdf9bb8..a39b78798d98 100644
--- a/mypy/build.py
+++ b/mypy/build.py
@@ -2447,13 +2447,14 @@ def find_module_and_diagnose(manager: BuildManager,
         # Don't honor a global (not per-module) ignore_missing_imports
         # setting for modules that used to have bundled stubs, as
         # otherwise updating mypy can silently result in new false
-        # negatives.
+        # negatives. (Unless there are stubs but they are incomplete.)
         global_ignore_missing_imports = manager.options.ignore_missing_imports
         py_ver = options.python_version[0]
         if ((is_legacy_bundled_package(top_level, py_ver)
                 or is_legacy_bundled_package(second_level, py_ver))
                 and global_ignore_missing_imports
-                and not options.ignore_missing_imports_per_module):
+                and not options.ignore_missing_imports_per_module
+                and result is ModuleNotFoundReason.APPROVED_STUBS_NOT_INSTALLED):
             ignore_missing_imports = False
 
         if skip_diagnose:
diff --git a/mypy/modulefinder.py b/mypy/modulefinder.py
index 4e608097289b..eb763652175e 100644
--- a/mypy/modulefinder.py
+++ b/mypy/modulefinder.py
@@ -230,10 +230,14 @@ def _find_module_non_stub_helper(self, components: List[str],
             elif not plausible_match and (self.fscache.isdir(dir_path)
                                           or self.fscache.isfile(dir_path + ".py")):
                 plausible_match = True
-        if (is_legacy_bundled_package(components[0], self.python_major_ver)
-                or is_legacy_bundled_package('.'.join(components[:2]), self.python_major_ver)):
+        if is_legacy_bundled_package(components[0], self.python_major_ver):
+            if (len(components) == 1
+                    or (self.find_module(components[0]) is
+                        ModuleNotFoundReason.APPROVED_STUBS_NOT_INSTALLED)):
+                return ModuleNotFoundReason.APPROVED_STUBS_NOT_INSTALLED
+        if is_legacy_bundled_package('.'.join(components[:2]), self.python_major_ver):
             return ModuleNotFoundReason.APPROVED_STUBS_NOT_INSTALLED
-        elif plausible_match:
+        if plausible_match:
             return ModuleNotFoundReason.FOUND_WITHOUT_TYPE_HINTS
         else:
             return ModuleNotFoundReason.NOT_FOUND
diff --git a/test-data/unit/check-modules.test b/test-data/unit/check-modules.test
index 9a68b00b6007..ad7322a2573f 100644
--- a/test-data/unit/check-modules.test
+++ b/test-data/unit/check-modules.test
@@ -3107,3 +3107,18 @@ from google.cloud import x
 main:1: error: Cannot find implementation or library stub for module named "google.cloud"
 main:1: note: See https://mypy.readthedocs.io/en/stable/running_mypy.html#missing-imports
 main:1: error: Cannot find implementation or library stub for module named "google"
+
+[case testMissingSubmoduleOfInstalledStubPackage]
+import bleach.xyz
+from bleach.abc import fgh
+[file bleach/__init__.pyi]
+[out]
+main:1: error: Cannot find implementation or library stub for module named "bleach.xyz"
+main:1: note: See https://mypy.readthedocs.io/en/stable/running_mypy.html#missing-imports
+main:2: error: Cannot find implementation or library stub for module named "bleach.abc"
+
+[case testMissingSubmoduleOfInstalledStubPackageIgnored]
+# flags: --ignore-missing-imports
+import bleach.xyz
+from bleach.abc import fgh
+[file bleach/__init__.pyi]