diff --git a/changelog/4046.bugfix.rst b/changelog/4046.bugfix.rst
new file mode 100644
index 0000000000..2b0da70cd0
--- /dev/null
+++ b/changelog/4046.bugfix.rst
@@ -0,0 +1 @@
+Fix problems with running tests in package ``__init__.py`` files.
diff --git a/src/_pytest/main.py b/src/_pytest/main.py
index f27270f262..2bb4050812 100644
--- a/src/_pytest/main.py
+++ b/src/_pytest/main.py
@@ -281,15 +281,6 @@ def pytest_ignore_collect(path, config):
     if _in_venv(path) and not allow_in_venv:
         return True
 
-    # Skip duplicate paths.
-    keepduplicates = config.getoption("keepduplicates")
-    duplicate_paths = config.pluginmanager._duplicatepaths
-    if not keepduplicates:
-        if path in duplicate_paths:
-            return True
-        else:
-            duplicate_paths.add(path)
-
     return False
 
 
@@ -551,7 +542,15 @@ def _collect(self, arg):
                 col = root._collectfile(argpath)
                 if col:
                     self._node_cache[argpath] = col
-            for y in self.matchnodes(col, names):
+            m = self.matchnodes(col, names)
+            # If __init__.py was the only file requested, then the matched node will be
+            # the corresponding Package, and the first yielded item will be the __init__
+            # Module itself, so just use that. If this special case isn't taken, then all
+            # the files in the package will be yielded.
+            if argpath.basename == "__init__.py":
+                yield next(m[0].collect())
+                return
+            for y in m:
                 yield y
 
     def _collectfile(self, path):
@@ -559,6 +558,16 @@ def _collectfile(self, path):
         if not self.isinitpath(path):
             if ihook.pytest_ignore_collect(path=path, config=self.config):
                 return ()
+
+        # Skip duplicate paths.
+        keepduplicates = self.config.getoption("keepduplicates")
+        if not keepduplicates:
+            duplicate_paths = self.config.pluginmanager._duplicatepaths
+            if path in duplicate_paths:
+                return ()
+            else:
+                duplicate_paths.add(path)
+
         return ihook.pytest_collect_file(path=path, parent=self)
 
     def _recurse(self, path):
diff --git a/src/_pytest/python.py b/src/_pytest/python.py
index 58f95034d2..414eabec6c 100644
--- a/src/_pytest/python.py
+++ b/src/_pytest/python.py
@@ -552,15 +552,6 @@ def isinitpath(self, path):
         return path in self.session._initialpaths
 
     def collect(self):
-        # XXX: HACK!
-        # Before starting to collect any files from this package we need
-        # to cleanup the duplicate paths added by the session's collect().
-        # Proper fix is to not track these as duplicates in the first place.
-        for path in list(self.session.config.pluginmanager._duplicatepaths):
-            # if path.parts()[:len(self.fspath.dirpath().parts())] == self.fspath.dirpath().parts():
-            if path.dirname.startswith(self.name):
-                self.session.config.pluginmanager._duplicatepaths.remove(path)
-
         this_path = self.fspath.dirpath()
         init_module = this_path.join("__init__.py")
         if init_module.check(file=1) and path_matches_patterns(
diff --git a/testing/test_collection.py b/testing/test_collection.py
index 7f6791dae9..06f8d40ee4 100644
--- a/testing/test_collection.py
+++ b/testing/test_collection.py
@@ -957,6 +957,21 @@ def test_collect_init_tests(testdir):
             "*<Function 'test_foo'>",
         ]
     )
+    result = testdir.runpytest("./tests", "--collect-only")
+    result.stdout.fnmatch_lines(
+        [
+            "*<Module '__init__.py'>",
+            "*<Function 'test_init'>",
+            "*<Module 'test_foo.py'>",
+            "*<Function 'test_foo'>",
+        ]
+    )
+    result = testdir.runpytest("./tests/test_foo.py", "--collect-only")
+    result.stdout.fnmatch_lines(["*<Module 'test_foo.py'>", "*<Function 'test_foo'>"])
+    assert "test_init" not in result.stdout.str()
+    result = testdir.runpytest("./tests/__init__.py", "--collect-only")
+    result.stdout.fnmatch_lines(["*<Module '__init__.py'>", "*<Function 'test_init'>"])
+    assert "test_foo" not in result.stdout.str()
 
 
 def test_collect_invalid_signature_message(testdir):
diff --git a/testing/test_session.py b/testing/test_session.py
index 6225a2c0db..c1785b9166 100644
--- a/testing/test_session.py
+++ b/testing/test_session.py
@@ -219,7 +219,7 @@ class TestY(TestX):
         started = reprec.getcalls("pytest_collectstart")
         finished = reprec.getreports("pytest_collectreport")
         assert len(started) == len(finished)
-        assert len(started) == 7  # XXX extra TopCollector
+        assert len(started) == 8
         colfail = [x for x in finished if x.failed]
         assert len(colfail) == 1