diff --git a/.coveragerc b/.coveragerc
index 2913b113..d7b2fedb 100644
--- a/.coveragerc
+++ b/.coveragerc
@@ -6,6 +6,7 @@ omit =
 	*/_itertools.py
 	*/_legacy.py
 	*/simple.py
+	*/_path.py
 
 [report]
 show_missing = True
diff --git a/CHANGES.rst b/CHANGES.rst
index 01e3a69f..6e3266ef 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -1,3 +1,15 @@
+v5.10.0
+=======
+
+* #203: Lifted restriction on modules passed to ``files``.
+  Now modules need not be a package and if a non-package
+  module is passed, resources will be resolved adjacent to
+  those modules, even for modules not found in any package.
+  For example, ``files(import_module('mod.py'))`` will
+  resolve resources found at the root. The parameter to
+  files was renamed from 'package' to 'anchor', with a
+  compatibility shim for those passing by keyword.
+
 v5.9.0
 ======
 
diff --git a/docs/index.rst b/docs/index.rst
index 7482611e..260696f9 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -6,8 +6,8 @@ in Python packages.  It provides functionality similar to ``pkg_resources``
 `Basic Resource Access`_ API, but without all of the overhead and performance
 problems of ``pkg_resources``.
 
-In our terminology, a *resource* is a file tree that is located within an
-importable `Python package`_.  Resources can live on the file system or in a
+In our terminology, a *resource* is a file tree that is located alongside an
+importable `Python module`_.  Resources can live on the file system or in a
 zip file, with support for other loader_ classes that implement the appropriate
 API for reading resources.
 
@@ -43,5 +43,5 @@ Indices and tables
 
 
 .. _`Basic Resource Access`: http://setuptools.readthedocs.io/en/latest/pkg_resources.html#basic-resource-access
-.. _`Python package`: https://docs.python.org/3/reference/import.html#packages
+.. _`Python module`: https://docs.python.org/3/glossary.html#term-module
 .. _loader: https://docs.python.org/3/reference/import.html#finders-and-loaders
diff --git a/docs/using.rst b/docs/using.rst
index 2b59b0cc..3403a6d9 100644
--- a/docs/using.rst
+++ b/docs/using.rst
@@ -5,11 +5,11 @@
 ===========================
 
 ``importlib_resources`` is a library that leverages Python's import system to
-provide access to *resources* within *packages*.  Given that this library is
-built on top of the import system, it is highly efficient and easy to use.
-This library's philosophy is that, if you can import a package, you can access
-resources within that package.  Resources can be opened or read, in either
-binary or text mode.
+provide access to *resources* within *packages* and alongside *modules*. Given
+that this library is built on top of the import system, it is highly efficient
+and easy to use. This library's philosophy is that, if one can import a
+module, one can access resources associated with that module. Resources can be
+opened or read, in either binary or text mode.
 
 What exactly do we mean by "a resource"?  It's easiest to think about the
 metaphor of files and directories on the file system, though it's important to
@@ -23,11 +23,14 @@ If you have a file system layout such as::
         one/
             __init__.py
             resource1.txt
+            module1.py
             resources1/
                 resource1.1.txt
         two/
             __init__.py
             resource2.txt
+    standalone.py
+    resource3.txt
 
 then the directories are ``data``, ``data/one``, and ``data/two``.  Each of
 these are also Python packages by virtue of the fact that they all contain
@@ -48,11 +51,14 @@ package directory, so
 ``data/one/resource1.txt`` and ``data/two/resource2.txt`` are both resources,
 as are the ``__init__.py`` files in all the directories.
 
-Resources are always accessed relative to the package that they live in.
-``resource1.txt`` and ``resources1/resource1.1.txt`` are resources within
-the ``data.one`` package, and
-``two/resource2.txt`` is a resource within the
-``data`` package.
+Resources in packages are always accessed relative to the package that they
+live in. ``resource1.txt`` and ``resources1/resource1.1.txt`` are resources
+within the ``data.one`` package, and ``two/resource2.txt`` is a resource
+within the ``data`` package.
+
+Resources may also be referenced relative to another *anchor*, a module in a
+package (``data.one.module1``) or a standalone module (``standalone``). In
+this case, resources are loaded from the same loader that loaded that module.
 
 
 Example
@@ -103,14 +109,14 @@ using ``importlib_resources`` would look like::
     eml = files('email.tests.data').joinpath('message.eml').read_text()
 
 
-Packages or package names
-=========================
+Anchors
+=======
 
-All of the ``importlib_resources`` APIs take a *package* as their first
-parameter, but this can either be a package name (as a ``str``) or an actual
-module object, though the module *must* be a package.  If a string is
-passed in, it must name an importable Python package, and this is first
-imported.  Thus the above example could also be written as::
+The ``importlib_resources`` ``files`` API takes an *anchor* as its first
+parameter, which can either be a package name (as a ``str``) or an actual
+module object.  If a string is passed in, it must name an importable Python
+module, which is imported prior to loading any resources. Thus the above
+example could also be written as::
 
     import email.tests.data
     eml = files(email.tests.data).joinpath('message.eml').read_text()
diff --git a/importlib_resources/_common.py b/importlib_resources/_common.py
index b8e2e1f0..52af4a13 100644
--- a/importlib_resources/_common.py
+++ b/importlib_resources/_common.py
@@ -5,20 +5,56 @@
 import contextlib
 import types
 import importlib
+import warnings
 
-from typing import Union, Optional
+from typing import Union, Optional, cast
 from .abc import ResourceReader, Traversable
 
 from ._compat import wrap_spec
 
 Package = Union[types.ModuleType, str]
+Anchor = Package
 
 
-def files(package: Package) -> Traversable:
+def package_to_anchor(func):
     """
-    Get a Traversable resource from a package
+    Replace 'package' parameter as 'anchor' and warn about the change.
+
+    Other errors should fall through.
+
+    >>> files()
+    Traceback (most recent call last):
+    TypeError: files() missing 1 required positional argument: 'anchor'
+    >>> files('a', 'b')
+    Traceback (most recent call last):
+    TypeError: files() takes 1 positional argument but 2 were given
+    """
+    undefined = object()
+
+    @functools.wraps(func)
+    def wrapper(anchor=undefined, package=undefined):
+        if package is not undefined:
+            if anchor is not undefined:
+                return func(anchor, package)
+            warnings.warn(
+                "First parameter to files is renamed to 'anchor'",
+                DeprecationWarning,
+                stacklevel=2,
+            )
+            return func(package)
+        elif anchor is undefined:
+            return func()
+        return func(anchor)
+
+    return wrapper
+
+
+@package_to_anchor
+def files(anchor: Anchor) -> Traversable:
+    """
+    Get a Traversable resource for an anchor.
     """
-    return from_package(get_package(package))
+    return from_package(resolve(anchor))
 
 
 def get_resource_reader(package: types.ModuleType) -> Optional[ResourceReader]:
@@ -38,27 +74,16 @@ def get_resource_reader(package: types.ModuleType) -> Optional[ResourceReader]:
 
 
 @functools.singledispatch
-def resolve(cand: Package):
-    return cand
+def resolve(cand: Anchor) -> types.ModuleType:
+    return cast(types.ModuleType, cand)
 
 
 @resolve.register
-def _(cand: str):
+def _(cand: str) -> types.ModuleType:
     return importlib.import_module(cand)
 
 
-def get_package(package: Package) -> types.ModuleType:
-    """Take a package name or module object and return the module.
-
-    Raise an exception if the resolved module is not a package.
-    """
-    resolved = resolve(package)
-    if wrap_spec(resolved).submodule_search_locations is None:
-        raise TypeError(f'{package!r} is not a package')
-    return resolved
-
-
-def from_package(package):
+def from_package(package: types.ModuleType):
     """
     Return a Traversable object for the given package.
 
diff --git a/importlib_resources/tests/_compat.py b/importlib_resources/tests/_compat.py
index 4c99cffd..e7bf06dd 100644
--- a/importlib_resources/tests/_compat.py
+++ b/importlib_resources/tests/_compat.py
@@ -6,7 +6,20 @@
 except ImportError:
     # Python 3.9 and earlier
     class import_helper:  # type: ignore
-        from test.support import modules_setup, modules_cleanup
+        from test.support import (
+            modules_setup,
+            modules_cleanup,
+            DirsOnSysPath,
+            CleanImport,
+        )
+
+
+try:
+    from test.support import os_helper  # type: ignore
+except ImportError:
+    # Python 3.9 compat
+    class os_helper:  # type:ignore
+        from test.support import temp_dir
 
 
 try:
diff --git a/importlib_resources/tests/_path.py b/importlib_resources/tests/_path.py
new file mode 100644
index 00000000..c630e4d3
--- /dev/null
+++ b/importlib_resources/tests/_path.py
@@ -0,0 +1,50 @@
+import pathlib
+import functools
+
+
+####
+# from jaraco.path 3.4
+
+
+def build(spec, prefix=pathlib.Path()):
+    """
+    Build a set of files/directories, as described by the spec.
+
+    Each key represents a pathname, and the value represents
+    the content. Content may be a nested directory.
+
+    >>> spec = {
+    ...     'README.txt': "A README file",
+    ...     "foo": {
+    ...         "__init__.py": "",
+    ...         "bar": {
+    ...             "__init__.py": "",
+    ...         },
+    ...         "baz.py": "# Some code",
+    ...     }
+    ... }
+    >>> tmpdir = getfixture('tmpdir')
+    >>> build(spec, tmpdir)
+    """
+    for name, contents in spec.items():
+        create(contents, pathlib.Path(prefix) / name)
+
+
+@functools.singledispatch
+def create(content, path):
+    path.mkdir(exist_ok=True)
+    build(content, prefix=path)  # type: ignore
+
+
+@create.register
+def _(content: bytes, path):
+    path.write_bytes(content)
+
+
+@create.register
+def _(content: str, path):
+    path.write_text(content)
+
+
+# end from jaraco.path
+####
diff --git a/importlib_resources/tests/test_files.py b/importlib_resources/tests/test_files.py
index 2676b49e..196469a3 100644
--- a/importlib_resources/tests/test_files.py
+++ b/importlib_resources/tests/test_files.py
@@ -1,10 +1,21 @@
 import typing
 import unittest
+import warnings
+import contextlib
 
 import importlib_resources as resources
 from importlib_resources.abc import Traversable
 from . import data01
 from . import util
+from . import _path
+from ._compat import os_helper, import_helper
+
+
+@contextlib.contextmanager
+def suppress_known_deprecation():
+    with warnings.catch_warnings(record=True) as ctx:
+        warnings.simplefilter('default', category=DeprecationWarning)
+        yield ctx
 
 
 class FilesTests:
@@ -25,6 +36,14 @@ def test_read_text(self):
     def test_traversable(self):
         assert isinstance(resources.files(self.data), Traversable)
 
+    def test_old_parameter(self):
+        """
+        Files used to take a 'package' parameter. Make sure anyone
+        passing by name is still supported.
+        """
+        with suppress_known_deprecation():
+            resources.files(package=self.data)
+
 
 class OpenDiskTests(FilesTests, unittest.TestCase):
     def setUp(self):
@@ -42,5 +61,28 @@ def setUp(self):
         self.data = namespacedata01
 
 
+class ModulesFilesTests(unittest.TestCase):
+    def setUp(self):
+        self.fixtures = contextlib.ExitStack()
+        self.addCleanup(self.fixtures.close)
+        self.site_dir = self.fixtures.enter_context(os_helper.temp_dir())
+        self.fixtures.enter_context(import_helper.DirsOnSysPath(self.site_dir))
+        self.fixtures.enter_context(import_helper.CleanImport())
+
+    def test_module_resources(self):
+        """
+        A module can have resources found adjacent to the module.
+        """
+        spec = {
+            'mod.py': '',
+            'res.txt': 'resources are the best',
+        }
+        _path.build(spec, self.site_dir)
+        import mod
+
+        actual = resources.files(mod).joinpath('res.txt').read_text()
+        assert actual == spec['res.txt']
+
+
 if __name__ == '__main__':
     unittest.main()
diff --git a/importlib_resources/tests/util.py b/importlib_resources/tests/util.py
index c6d83e4b..3c36a9d2 100644
--- a/importlib_resources/tests/util.py
+++ b/importlib_resources/tests/util.py
@@ -102,17 +102,6 @@ def test_importing_module_as_side_effect(self):
         del sys.modules[data01.__name__]
         self.execute(data01.__name__, 'utf-8.file')
 
-    def test_non_package_by_name(self):
-        # The anchor package cannot be a module.
-        with self.assertRaises(TypeError):
-            self.execute(__name__, 'utf-8.file')
-
-    def test_non_package_by_package(self):
-        # The anchor package cannot be a module.
-        with self.assertRaises(TypeError):
-            module = sys.modules['importlib_resources.tests.util']
-            self.execute(module, 'utf-8.file')
-
     def test_missing_path(self):
         # Attempting to open or read or request the path for a
         # non-existent path should succeed if open_resource