diff --git a/CHANGES.rst b/CHANGES.rst
index 7e9c69383..856731d02 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -22,10 +22,16 @@ This list is detailed and covers changes in each pre-release version.
 Unreleased
 ----------
 
-- Fix: the sticky header on the HTML report didn't work unless you had branch
-  coverage enabled. This is now fixed, the sticky header works for everyone.
+- Fix: The sticky header on the HTML report didn't work unless you had branch
+  coverage enabled. This is now fixed: the sticky header works for everyone.
   (Do people still use coverage without branch measurement!? j/k)
 
+- Fix: When using explicitly declared namespace packages, the "already imported
+  a file that will be measured" warning would be issued (`issue 888`_).  This
+  is now fixed.
+
+.. _issue 888: https://github.com/nedbat/coveragepy/issues/888
+
 
 .. _changes_61:
 
diff --git a/coverage/inorout.py b/coverage/inorout.py
index 3bc7e54e4..8badf4f77 100644
--- a/coverage/inorout.py
+++ b/coverage/inorout.py
@@ -479,6 +479,10 @@ def warn_already_imported_files(self):
                 if filename in warned:
                     continue
 
+                if len(getattr(mod, "__path__", ())) > 1:
+                    # A namespace package, which confuses this code, so ignore it.
+                    continue
+
                 disp = self.should_trace(filename)
                 if disp.has_dynamic_filename:
                     # A plugin with dynamic filenames: the Python file
diff --git a/lab/treetopy.sh b/lab/treetopy.sh
new file mode 100644
index 000000000..2dcf1cac3
--- /dev/null
+++ b/lab/treetopy.sh
@@ -0,0 +1,6 @@
+# Turn a tree of Python files into a series of make_file calls.
+for f in **/*.py; do
+    echo 'make_file("'$1$f'", """\\'
+    sed -e 's/^/    /' <$f
+    echo '    """)'
+done
diff --git a/tests/test_venv.py b/tests/test_venv.py
index e66103372..c9c204973 100644
--- a/tests/test_venv.py
+++ b/tests/test_venv.py
@@ -84,7 +84,6 @@ def fifth(x):
             def sixth(x):
                 return 6 * x
             """)
-        # The setup.py to install everything.
         make_file("another_pkg/setup.py", """\
             import setuptools
             setuptools.setup(
@@ -93,9 +92,52 @@ def sixth(x):
             )
             """)
 
+        # Bug888 code.
+        make_file("bug888/app/setup.py", """\
+            from setuptools import setup
+            setup(
+                name='testcov',
+                packages=['testcov'],
+                namespace_packages=['testcov'],
+            )
+            """)
+        make_file("bug888/app/testcov/__init__.py", """\
+            try:  # pragma: no cover
+                __import__('pkg_resources').declare_namespace(__name__)
+            except ImportError:  # pragma: no cover
+                from pkgutil import extend_path
+                __path__ = extend_path(__path__, __name__)
+            """)
+        make_file("bug888/app/testcov/main.py", """\
+            import pkg_resources
+            for entry_point in pkg_resources.iter_entry_points('plugins'):
+                entry_point.load()()
+            """)
+        make_file("bug888/plugin/setup.py", """\
+            from setuptools import setup
+            setup(
+                name='testcov-plugin',
+                packages=['testcov'],
+                namespace_packages=['testcov'],
+                entry_points={'plugins': ['testp = testcov.plugin:testp']},
+            )
+            """)
+        make_file("bug888/plugin/testcov/__init__.py", """\
+            try:  # pragma: no cover
+                __import__('pkg_resources').declare_namespace(__name__)
+            except ImportError:  # pragma: no cover
+                from pkgutil import extend_path
+                __path__ = extend_path(__path__, __name__)
+            """)
+        make_file("bug888/plugin/testcov/plugin.py", """\
+            def testp():
+                print("Plugin here")
+            """)
+
         # Install the third-party packages.
         run_in_venv("python -m pip install --no-index ./third_pkg")
         run_in_venv("python -m pip install --no-index -e ./another_pkg")
+        run_in_venv("python -m pip install --no-index -e ./bug888/app -e ./bug888/plugin")
         shutil.rmtree("third_pkg")
 
         # Install coverage.
@@ -141,7 +183,7 @@ def in_venv_world_fixture(self, venv_world):
             yield
 
             for fname in os.listdir("."):
-                if fname not in {"venv", "another_pkg"}:
+                if fname not in {"venv", "another_pkg", "bug888"}:
                     os.remove(fname)
 
     def get_trace_output(self):
@@ -274,3 +316,11 @@ def test_installed_namespace_packages(self, coverage_command):
         assert "colorsys" not in out
         assert "fifth" in out
         assert "sixth" in out
+
+    def test_bug888(self, coverage_command):
+        out = run_in_venv(
+            coverage_command +
+            " run --source=bug888/app,bug888/plugin bug888/app/testcov/main.py"
+            )
+        # When the test fails, the output includes "Already imported a file that will be measured"
+        assert out == "Plugin here\n"