diff --git a/changelog/3796.bugfix.rst b/changelog/3796.bugfix.rst
new file mode 100644
index 000000000..7a115301a
--- /dev/null
+++ b/changelog/3796.bugfix.rst
@@ -0,0 +1,2 @@
+Fixed an issue where teardown of fixtures of consecutive sub-packages were executed once, at the end of the outer
+package.
diff --git a/changelog/3854.bugfix.rst b/changelog/3854.bugfix.rst
new file mode 100644
index 000000000..6184f03b6
--- /dev/null
+++ b/changelog/3854.bugfix.rst
@@ -0,0 +1 @@
+Fixes double collection of tests within packages when the filename starts with a capital letter.
diff --git a/src/_pytest/fixtures.py b/src/_pytest/fixtures.py
index c12691caa..bfbf7bb54 100644
--- a/src/_pytest/fixtures.py
+++ b/src/_pytest/fixtures.py
@@ -2,7 +2,6 @@ from __future__ import absolute_import, division, print_function
 
 import functools
 import inspect
-import os
 import sys
 import warnings
 from collections import OrderedDict, deque, defaultdict
@@ -93,7 +92,7 @@ def get_scope_package(node, fixturedef):
 
     cls = pytest.Package
     current = node
-    fixture_package_name = os.path.join(fixturedef.baseid, "__init__.py")
+    fixture_package_name = "%s/%s" % (fixturedef.baseid, "__init__.py")
     while current and (
         type(current) is not cls or fixture_package_name != current.nodeid
     ):
diff --git a/src/_pytest/python.py b/src/_pytest/python.py
index 45ef3be61..7fb7ff9ef 100644
--- a/src/_pytest/python.py
+++ b/src/_pytest/python.py
@@ -590,17 +590,28 @@ class Package(Module):
                 self.session.config.pluginmanager._duplicatepaths.remove(path)
 
         this_path = self.fspath.dirpath()
-        pkg_prefix = None
+        pkg_prefixes = set()
         for path in this_path.visit(rec=self._recurse, bf=True, sort=True):
             # we will visit our own __init__.py file, in which case we skip it
+            skip = False
             if path.basename == "__init__.py" and path.dirpath() == this_path:
                 continue
-            if pkg_prefix and pkg_prefix in path.parts():
+
+            for pkg_prefix in pkg_prefixes:
+                if (
+                    pkg_prefix in path.parts()
+                    and pkg_prefix.join("__init__.py") != path
+                ):
+                    skip = True
+
+            if skip:
                 continue
+
+            if path.isdir() and path.join("__init__.py").check(file=1):
+                pkg_prefixes.add(path)
+
             for x in self._collectfile(path):
                 yield x
-                if isinstance(x, Package):
-                    pkg_prefix = path.dirpath()
 
 
 def _get_xunit_setup_teardown(holder, attr_name, param_obj=None):
diff --git a/testing/python/collect.py b/testing/python/collect.py
index b3b19802a..8f4283e40 100644
--- a/testing/python/collect.py
+++ b/testing/python/collect.py
@@ -1624,3 +1624,38 @@ def test_package_with_modules(testdir):
     root.chdir()
     result = testdir.runpytest("-v", "-s")
     result.assert_outcomes(passed=2)
+
+
+def test_package_ordering(testdir):
+    """
+    .
+    └── root
+        ├── Test_root.py
+        ├── __init__.py
+        ├── sub1
+        │   ├── Test_sub1.py
+        │   └── __init__.py
+        └── sub2
+            └── test
+                └── test_sub2.py
+
+    """
+    testdir.makeini(
+        """
+        [pytest]
+        python_files=*.py
+    """
+    )
+    root = testdir.mkpydir("root")
+    sub1 = root.mkdir("sub1")
+    sub1.ensure("__init__.py")
+    sub2 = root.mkdir("sub2")
+    sub2_test = sub2.mkdir("sub2")
+
+    root.join("Test_root.py").write("def test_1(): pass")
+    sub1.join("Test_sub1.py").write("def test_2(): pass")
+    sub2_test.join("test_sub2.py").write("def test_3(): pass")
+
+    # Execute from .
+    result = testdir.runpytest("-v", "-s")
+    result.assert_outcomes(passed=3)
diff --git a/testing/python/fixture.py b/testing/python/fixture.py
index 47be7800c..f8f5eb54e 100644
--- a/testing/python/fixture.py
+++ b/testing/python/fixture.py
@@ -1,3 +1,4 @@
+# -*- coding: utf-8 -*-
 import textwrap
 
 import pytest
@@ -3977,3 +3978,71 @@ class TestScopeOrdering(object):
         items, _ = testdir.inline_genitems()
         request = FixtureRequest(items[0])
         assert request.fixturenames == "s1 p1 m1 m2 c1 f2 f1".split()
+
+    def test_multiple_packages(self, testdir):
+        """Complex test involving multiple package fixtures. Make sure teardowns
+        are executed in order.
+        .
+        └── root
+            ├── __init__.py
+            ├── sub1
+            │   ├── __init__.py
+            │   ├── conftest.py
+            │   └── test_1.py
+            └── sub2
+                ├── __init__.py
+                ├── conftest.py
+                └── test_2.py
+        """
+        root = testdir.mkdir("root")
+        root.join("__init__.py").write("values = []")
+        sub1 = root.mkdir("sub1")
+        sub1.ensure("__init__.py")
+        sub1.join("conftest.py").write(
+            textwrap.dedent(
+                """\
+            import pytest
+            from .. import values
+            @pytest.fixture(scope="package")
+            def fix():
+                values.append("pre-sub1")
+                yield values
+                assert values.pop() == "pre-sub1"
+        """
+            )
+        )
+        sub1.join("test_1.py").write(
+            textwrap.dedent(
+                """\
+            from .. import values
+            def test_1(fix):
+                assert values == ["pre-sub1"]
+        """
+            )
+        )
+        sub2 = root.mkdir("sub2")
+        sub2.ensure("__init__.py")
+        sub2.join("conftest.py").write(
+            textwrap.dedent(
+                """\
+            import pytest
+            from .. import values
+            @pytest.fixture(scope="package")
+            def fix():
+                values.append("pre-sub2")
+                yield values
+                assert values.pop() == "pre-sub2"
+        """
+            )
+        )
+        sub2.join("test_2.py").write(
+            textwrap.dedent(
+                """\
+            from .. import values
+            def test_2(fix):
+                assert values == ["pre-sub2"]
+        """
+            )
+        )
+        reprec = testdir.inline_run()
+        reprec.assertoutcome(passed=2)