diff --git a/importlib_metadata/__init__.py b/importlib_metadata/__init__.py
index 61325221..c2c4b1e9 100644
--- a/importlib_metadata/__init__.py
+++ b/importlib_metadata/__init__.py
@@ -19,6 +19,7 @@
 import posixpath
 import collections
 
+from .compat.py38 import relative_fix
 from . import _adapters, _meta, _py39compat
 from ._collections import FreezableDefaultDict, Pair
 from ._compat import (
@@ -562,31 +563,14 @@ def _read_files_egginfo_installed(self):
         if not text or not subdir:
             return
 
-        site_path = self.locate_file('').resolve()
         paths = (
-            self._relative_to(
-                (subdir / name).resolve(),
-                site_path,
-            ).as_posix()
+            relative_fix((subdir / name).resolve())
+            .relative_to(self.locate_file('').resolve(), walk_up=True)
+            .as_posix()
             for name in text.splitlines()
         )
         return map('"{}"'.format, paths)
 
-    def _relative_to(self, path, root):
-        """
-        Workaround for https://github.com/python/cpython/issues/67271 where ".."
-        isn't added by pathlib.Path.relative_to() when path is not
-        a subpath of root.
-
-        One example of such a package is dask-labextension, which uses
-        jupyter-packaging to install JupyterLab javascript files outside
-        of site-packages.
-        """
-        try:
-            return path.relative_to(root)
-        except ValueError:
-            return pathlib.Path(os.path.relpath(path, root))
-
     def _read_files_egginfo_sources(self):
         """
         Read SOURCES.txt and return lines in a similar CSV-parsable
diff --git a/importlib_metadata/compat/py38.py b/importlib_metadata/compat/py38.py
new file mode 100644
index 00000000..2499c3f6
--- /dev/null
+++ b/importlib_metadata/compat/py38.py
@@ -0,0 +1,23 @@
+import os
+import pathlib
+import sys
+import types
+
+
+def wrap(path):
+    """
+    Workaround for https://github.com/python/cpython/issues/67271 where ".."
+    isn't added by pathlib.Path.relative_to() when path is not
+    a subpath of root.
+    One example of such a package is dask-labextension, which uses
+    jupyter-packaging to install JupyterLab javascript files outside
+    of site-packages.
+    """
+
+    def relative_to(root, *, walk_up=False):
+        return pathlib.Path(os.path.relpath(path, root))
+
+    return types.SimpleNamespace(relative_to=relative_to)
+
+
+relative_fix = wrap if sys.version_info < (3, 9) else lambda x: x