diff --git a/sphinx/apidoc.py b/sphinx/apidoc.py
index 3b51469d1..06cbfa026 100644
--- a/sphinx/apidoc.py
+++ b/sphinx/apidoc.py
@@ -16,6 +16,7 @@
 """
 from __future__ import print_function
 
+import glob
 import os
 import sys
 import optparse
@@ -194,7 +195,17 @@ def shall_skip(module, opts):
 
     # skip it if there is nothing (or just \n or \r\n) in the file
     if path.exists(module) and path.getsize(module) <= 2:
-        return True
+        skip = True
+        if os.path.basename(module) == '__init__.py':
+            pattern = path.join(path.dirname(module), '*.py')
+            # We only want to skip packages if they do not contain any
+            # .py files other than __init__.py.
+            other_modules = list(glob.glob(pattern))
+            other_modules.remove(module)
+            skip = not other_modules
+
+        if skip:
+            return True
 
     # skip if it has a "private" name and this is selected
     filename = path.basename(module)
diff --git a/tests/roots/test-apidoc-pep420/a/b/e/__init__.py b/tests/roots/test-apidoc-pep420/a/b/e/__init__.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/tests/roots/test-apidoc-pep420/a/b/e/f.py b/tests/roots/test-apidoc-pep420/a/b/e/f.py
new file mode 100644
index 000000000..a09affe86
--- /dev/null
+++ b/tests/roots/test-apidoc-pep420/a/b/e/f.py
@@ -0,0 +1 @@
+"Module f"
diff --git a/tests/test_apidoc.py b/tests/test_apidoc.py
index f5037ab71..e7f986df3 100644
--- a/tests/test_apidoc.py
+++ b/tests/test_apidoc.py
@@ -67,6 +67,7 @@ def test_pep_0420_enabled(make_app, apidoc):
     outdir = apidoc.outdir
     assert (outdir / 'conf.py').isfile()
     assert (outdir / 'a.b.c.rst').isfile()
+    assert (outdir / 'a.b.e.rst').isfile()
     assert (outdir / 'a.b.x.rst').isfile()
 
     with open(outdir / 'a.b.c.rst') as f:
@@ -74,6 +75,10 @@ def test_pep_0420_enabled(make_app, apidoc):
         assert "automodule:: a.b.c.d\n" in rst
         assert "automodule:: a.b.c\n" in rst
 
+    with open(outdir / 'a.b.e.rst') as f:
+        rst = f.read()
+        assert "automodule:: a.b.e.f\n" in rst
+
     with open(outdir / 'a.b.x.rst') as f:
         rst = f.read()
         assert "automodule:: a.b.x.y\n" in rst
@@ -86,12 +91,67 @@ def test_pep_0420_enabled(make_app, apidoc):
 
     builddir = outdir / '_build' / 'text'
     assert (builddir / 'a.b.c.txt').isfile()
+    assert (builddir / 'a.b.e.txt').isfile()
     assert (builddir / 'a.b.x.txt').isfile()
 
     with open(builddir / 'a.b.c.txt') as f:
         txt = f.read()
         assert "a.b.c package\n" in txt
 
+    with open(builddir / 'a.b.e.txt') as f:
+        txt = f.read()
+        assert "a.b.e.f module\n" in txt
+
+    with open(builddir / 'a.b.x.txt') as f:
+        txt = f.read()
+        assert "a.b.x namespace\n" in txt
+
+
+@pytest.mark.apidoc(
+    coderoot='test-apidoc-pep420',
+    options=["--implicit-namespaces", "--separate"],
+)
+def test_pep_0420_enabled_separate(make_app, apidoc):
+    outdir = apidoc.outdir
+    assert (outdir / 'conf.py').isfile()
+    assert (outdir / 'a.b.c.rst').isfile()
+    assert (outdir / 'a.b.e.rst').isfile()
+    assert (outdir / 'a.b.e.f.rst').isfile()
+    assert (outdir / 'a.b.x.rst').isfile()
+    assert (outdir / 'a.b.x.y.rst').isfile()
+
+    with open(outdir / 'a.b.c.rst') as f:
+        rst = f.read()
+        assert ".. toctree::\n\n   a.b.c.d\n" in rst
+
+    with open(outdir / 'a.b.e.rst') as f:
+        rst = f.read()
+        assert ".. toctree::\n\n   a.b.e.f\n" in rst
+
+    with open(outdir / 'a.b.x.rst') as f:
+        rst = f.read()
+        assert ".. toctree::\n\n   a.b.x.y\n" in rst
+
+    app = make_app('text', srcdir=outdir)
+    app.build()
+    print(app._status.getvalue())
+    print(app._warning.getvalue())
+
+    builddir = outdir / '_build' / 'text'
+    assert (builddir / 'a.b.c.txt').isfile()
+    assert (builddir / 'a.b.e.txt').isfile()
+    assert (builddir / 'a.b.e.f.txt').isfile()
+    assert (builddir / 'a.b.x.txt').isfile()
+    assert (builddir / 'a.b.x.y.txt').isfile()
+
+    with open(builddir / 'a.b.c.txt') as f:
+        txt = f.read()
+        assert "a.b.c package\n" in txt
+
+    with open(builddir / 'a.b.e.f.txt') as f:
+        txt = f.read()
+        assert "a.b.e.f module\n" in txt
+
     with open(builddir / 'a.b.x.txt') as f:
         txt = f.read()
         assert "a.b.x namespace\n" in txt