diff --git a/mypy/modulefinder.py b/mypy/modulefinder.py
index bd331c7dbe78..1cbdf7a04604 100644
--- a/mypy/modulefinder.py
+++ b/mypy/modulefinder.py
@@ -212,6 +212,7 @@ def _find_module(self, id: str) -> Optional[str]:
         near_misses = []  # Collect near misses for namespace mode (see below).
         for base_dir, verify in candidate_base_dirs:
             base_path = base_dir + seplast  # so e.g. '/usr/lib/python3.4/foo/bar/baz'
+            has_init = False
             dir_prefix = base_dir
             for _ in range(len(components) - 1):
                 dir_prefix = os.path.dirname(dir_prefix)
@@ -220,6 +221,7 @@ def _find_module(self, id: str) -> Optional[str]:
                 path = base_path + sepinit + extension
                 path_stubs = base_path + '-stubs' + sepinit + extension
                 if fscache.isfile_case(path, dir_prefix):
+                    has_init = True
                     if verify and not verify_module(fscache, id, path, dir_prefix):
                         near_misses.append((path, dir_prefix))
                         continue
@@ -229,8 +231,12 @@ def _find_module(self, id: str) -> Optional[str]:
                         near_misses.append((path_stubs, dir_prefix))
                         continue
                     return path_stubs
-                elif self.options and self.options.namespace_packages and fscache.isdir(base_path):
+
+            # In namespace mode, register a potential namespace package
+            if self.options and self.options.namespace_packages:
+                if fscache.isdir(base_path) and not has_init:
                     near_misses.append((base_path, dir_prefix))
+
             # No package, look for module.
             for extension in PYTHON_EXTENSIONS:
                 path = base_path + extension
diff --git a/mypy/test/testmodulefinder.py b/mypy/test/testmodulefinder.py
new file mode 100644
index 000000000000..ab1a0d8e67f4
--- /dev/null
+++ b/mypy/test/testmodulefinder.py
@@ -0,0 +1,136 @@
+import os
+
+from mypy.options import Options
+from mypy.modulefinder import FindModuleCache, SearchPaths
+
+from mypy.test.helpers import Suite, assert_equal
+from mypy.test.config import package_path
+data_path = os.path.relpath(os.path.join(package_path, "modulefinder"))
+
+
+class ModuleFinderSuite(Suite):
+
+    def setUp(self) -> None:
+        self.search_paths = SearchPaths(
+            python_path=(),
+            mypy_path=(
+                os.path.join(data_path, "nsx-pkg1"),
+                os.path.join(data_path, "nsx-pkg2"),
+                os.path.join(data_path, "nsx-pkg3"),
+                os.path.join(data_path, "nsy-pkg1"),
+                os.path.join(data_path, "nsy-pkg2"),
+                os.path.join(data_path, "pkg1"),
+                os.path.join(data_path, "pkg2"),
+            ),
+            package_path=(),
+            typeshed_path=(),
+        )
+        options = Options()
+        options.namespace_packages = True
+        self.fmc_ns = FindModuleCache(self.search_paths, options=options)
+
+        options = Options()
+        options.namespace_packages = False
+        self.fmc_nons = FindModuleCache(self.search_paths, options=options)
+
+    def test__no_namespace_packages__nsx(self) -> None:
+        """
+        If namespace_packages is False, we shouldn't find nsx
+        """
+        found_module = self.fmc_nons.find_module("nsx")
+        self.assertIsNone(found_module)
+
+    def test__no_namespace_packages__nsx_a(self) -> None:
+        """
+        If namespace_packages is False, we shouldn't find nsx.a.
+        """
+        found_module = self.fmc_nons.find_module("nsx.a")
+        self.assertIsNone(found_module)
+
+    def test__no_namespace_packages__find_a_in_pkg1(self) -> None:
+        """
+        Find find pkg1/a.py for "a" with namespace_packages False.
+        """
+        found_module = self.fmc_nons.find_module("a")
+        expected = os.path.join(data_path, "pkg1", "a.py")
+        assert_equal(expected, found_module)
+
+    def test__no_namespace_packages__find_b_in_pkg2(self) -> None:
+        found_module = self.fmc_ns.find_module("b")
+        expected = os.path.join(data_path, "pkg2", "b", "__init__.py")
+        assert_equal(expected, found_module)
+
+    def test__find_nsx_as_namespace_pkg_in_pkg1(self) -> None:
+        """
+        There's no __init__.py in any of the nsx dirs, return
+        the path to the first one found in mypypath.
+        """
+        found_module = self.fmc_ns.find_module("nsx")
+        expected = os.path.join(data_path, "nsx-pkg1", "nsx")
+        assert_equal(expected, found_module)
+
+    def test__find_nsx_a_init_in_pkg1(self) -> None:
+        """
+        Find nsx-pkg1/nsx/a/__init__.py for "nsx.a" in namespace mode.
+        """
+        found_module = self.fmc_ns.find_module("nsx.a")
+        expected = os.path.join(data_path, "nsx-pkg1", "nsx", "a", "__init__.py")
+        assert_equal(expected, found_module)
+
+    def test__find_nsx_b_init_in_pkg2(self) -> None:
+        """
+        Find nsx-pkg2/nsx/b/__init__.py for "nsx.b" in namespace mode.
+        """
+        found_module = self.fmc_ns.find_module("nsx.b")
+        expected = os.path.join(data_path, "nsx-pkg2", "nsx", "b", "__init__.py")
+        assert_equal(expected, found_module)
+
+    def test__find_nsx_c_c_in_pkg3(self) -> None:
+        """
+        Find nsx-pkg3/nsx/c/c.py for "nsx.c.c" in namespace mode.
+        """
+        found_module = self.fmc_ns.find_module("nsx.c.c")
+        expected = os.path.join(data_path, "nsx-pkg3", "nsx", "c", "c.py")
+        assert_equal(expected, found_module)
+
+    def test__find_nsy_a__init_pyi(self) -> None:
+        """
+        Prefer nsy-pkg1/a/__init__.pyi file over __init__.py.
+        """
+        found_module = self.fmc_ns.find_module("nsy.a")
+        expected = os.path.join(data_path, "nsy-pkg1", "nsy", "a", "__init__.pyi")
+        assert_equal(expected, found_module)
+
+    def test__find_nsy_b__init_py(self) -> None:
+        """
+        There is a nsy-pkg2/nsy/b.pyi, but also a nsy-pkg2/nsy/b/__init__.py.
+        We expect to find the latter when looking up "nsy.b" as
+        a package is preferred over a module.
+        """
+        found_module = self.fmc_ns.find_module("nsy.b")
+        expected = os.path.join(data_path, "nsy-pkg2", "nsy", "b", "__init__.py")
+        assert_equal(expected, found_module)
+
+    def test__find_nsy_c_pyi(self) -> None:
+        """
+        There is a nsy-pkg2/nsy/c.pyi and nsy-pkg2/nsy/c.py
+        We expect to find the former when looking up "nsy.b" as
+        .pyi is preferred over .py.
+        """
+        found_module = self.fmc_ns.find_module("nsy.c")
+        expected = os.path.join(data_path, "nsy-pkg2", "nsy", "c.pyi")
+        assert_equal(expected, found_module)
+
+    def test__find_a_in_pkg1(self) -> None:
+        found_module = self.fmc_ns.find_module("a")
+        expected = os.path.join(data_path, "pkg1", "a.py")
+        assert_equal(expected, found_module)
+
+    def test__find_b_init_in_pkg2(self) -> None:
+        found_module = self.fmc_ns.find_module("b")
+        expected = os.path.join(data_path, "pkg2", "b", "__init__.py")
+        assert_equal(expected, found_module)
+
+    def test__find_d_nowhere(self) -> None:
+        found_module = self.fmc_ns.find_module("d")
+        self.assertIsNone(found_module)
diff --git a/test-data/packages/modulefinder/nsx-pkg1/nsx/a/__init__.py b/test-data/packages/modulefinder/nsx-pkg1/nsx/a/__init__.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/test-data/packages/modulefinder/nsx-pkg2/nsx/b/__init__.py b/test-data/packages/modulefinder/nsx-pkg2/nsx/b/__init__.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/test-data/packages/modulefinder/nsx-pkg3/nsx/c/c.py b/test-data/packages/modulefinder/nsx-pkg3/nsx/c/c.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/test-data/packages/modulefinder/nsy-pkg1/nsy/a/__init__.py b/test-data/packages/modulefinder/nsy-pkg1/nsy/a/__init__.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/test-data/packages/modulefinder/nsy-pkg1/nsy/a/__init__.pyi b/test-data/packages/modulefinder/nsy-pkg1/nsy/a/__init__.pyi
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/test-data/packages/modulefinder/nsy-pkg2/nsy/b.pyi b/test-data/packages/modulefinder/nsy-pkg2/nsy/b.pyi
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/test-data/packages/modulefinder/nsy-pkg2/nsy/b/__init__.py b/test-data/packages/modulefinder/nsy-pkg2/nsy/b/__init__.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/test-data/packages/modulefinder/nsy-pkg2/nsy/c.py b/test-data/packages/modulefinder/nsy-pkg2/nsy/c.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/test-data/packages/modulefinder/nsy-pkg2/nsy/c.pyi b/test-data/packages/modulefinder/nsy-pkg2/nsy/c.pyi
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/test-data/packages/modulefinder/pkg1/a.py b/test-data/packages/modulefinder/pkg1/a.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/test-data/packages/modulefinder/pkg2/b/__init__.py b/test-data/packages/modulefinder/pkg2/b/__init__.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/test-data/packages/modulefinder/readme.txt b/test-data/packages/modulefinder/readme.txt
new file mode 100644
index 000000000000..669bcfcd2663
--- /dev/null
+++ b/test-data/packages/modulefinder/readme.txt
@@ -0,0 +1,4 @@
+Samples for testing modulefinder.FindModuleCache.
+
+Contains three packages for the `nsx` namespace, and two packages
+providing `a` and `b`.