diff --git a/src/whitenoise/storage.py b/src/whitenoise/storage.py
index ae3d7de7..029b0ff8 100644
--- a/src/whitenoise/storage.py
+++ b/src/whitenoise/storage.py
@@ -4,6 +4,10 @@
 import os
 import re
 import textwrap
+from typing import Any
+from typing import Iterator
+from typing import Tuple
+from typing import Union
 
 from django.conf import settings
 from django.contrib.staticfiles.storage import ManifestStaticFilesStorage
@@ -11,52 +15,33 @@
 
 from .compress import Compressor
 
+_PostProcessT = Iterator[Union[Tuple[str, str, bool], Tuple[str, None, RuntimeError]]]
 
-class CompressedStaticFilesMixin:
+
+class CompressedStaticFilesStorage(StaticFilesStorage):
     """
-    Wraps a StaticFilesStorage instance to compress output files
+    StaticFilesStorage subclass that compresses output files.
     """
 
-    def post_process(self, *args, **kwargs):
-        super_post_process = getattr(
-            super(),
-            "post_process",
-            self.fallback_post_process,
-        )
-        files = super_post_process(*args, **kwargs)
-        if not kwargs.get("dry_run"):
-            files = self.post_process_with_compression(files)
-        return files
-
-    # Only used if the class we're wrapping doesn't implement its own
-    # `post_process` method
-    def fallback_post_process(self, paths, dry_run=False, **options):
-        if not dry_run:
-            for path in paths:
-                yield path, None, False
+    def post_process(
+        self, paths: dict[str, Any], dry_run: bool = False, **options: Any
+    ) -> _PostProcessT:
+        if dry_run:
+            return
 
-    def create_compressor(self, **kwargs):
-        return Compressor(**kwargs)
-
-    def post_process_with_compression(self, files):
         extensions = getattr(settings, "WHITENOISE_SKIP_COMPRESS_EXTENSIONS", None)
         compressor = self.create_compressor(extensions=extensions, quiet=True)
-        for name, hashed_name, processed in files:
-            yield name, hashed_name, processed
-            if isinstance(processed, Exception):
-                continue
-            unique_names = set(filter(None, [name, hashed_name]))
-            for name in unique_names:
-                if compressor.should_compress(name):
-                    path = self.path(name)
-                    prefix_len = len(path) - len(name)
-                    for compressed_path in compressor.compress(path):
-                        compressed_name = compressed_path[prefix_len:]
-                        yield name, compressed_name, True
-
-
-class CompressedStaticFilesStorage(CompressedStaticFilesMixin, StaticFilesStorage):
-    pass
+
+        for path in paths:
+            if compressor.should_compress(path):
+                full_path = self.path(path)
+                prefix_len = len(full_path) - len(path)
+                for compressed_path in compressor.compress(full_path):
+                    compressed_name = compressed_path[prefix_len:]
+                    yield path, compressed_name, True
+
+    def create_compressor(self, **kwargs: Any) -> Compressor:
+        return Compressor(**kwargs)
 
 
 class MissingFileError(ValueError):
diff --git a/tests/test_storage.py b/tests/test_storage.py
index baf043e3..fca9a60f 100644
--- a/tests/test_storage.py
+++ b/tests/test_storage.py
@@ -48,7 +48,7 @@ def _compressed_storage(setup):
         storages = {"STATICFILES_STORAGE": backend}
 
     with override_settings(**storages):
-        call_command("collectstatic", verbosity=0, interactive=False)
+        yield
 
 
 @pytest.fixture()
@@ -68,12 +68,22 @@ def _compressed_manifest_storage(setup):
         call_command("collectstatic", verbosity=0, interactive=False)
 
 
-def test_compressed_files_are_created(_compressed_storage):
+def test_compressed_static_files_storage(_compressed_storage):
+    call_command("collectstatic", verbosity=0, interactive=False)
+
     for name in ["styles.css.gz", "styles.css.br"]:
         path = os.path.join(settings.STATIC_ROOT, name)
         assert os.path.exists(path)
 
 
+def test_compressed_static_files_storage_dry_run(_compressed_storage):
+    call_command("collectstatic", "--dry-run", verbosity=0, interactive=False)
+
+    for name in ["styles.css.gz", "styles.css.br"]:
+        path = os.path.join(settings.STATIC_ROOT, name)
+        assert not os.path.exists(path)
+
+
 def test_make_helpful_exception(_compressed_manifest_storage):
     class TriggerException(HashedFilesMixin):
         def exists(self, path):