diff --git a/pooch/processors.py b/pooch/processors.py
index 06bfb9fb..a4a0a6e8 100644
--- a/pooch/processors.py
+++ b/pooch/processors.py
@@ -76,8 +76,9 @@ def __call__(self, fname, action, pooch):
             )
         if self.extract_dir is None:
             self.extract_dir = fname + self.suffix
-        elif self.suffix is not None:
-            get_logger().warn("Ignoring 'suffix' because 'extract_dir' was provided.")
+        else:
+            archive_dir = fname.rsplit(os.path.sep, maxsplit=1)[0]
+            self.extract_dir = os.path.join(archive_dir, self.extract_dir)
         if action in ("update", "download") or not os.path.exists(self.extract_dir):
             # Make sure that the folder with the extracted files exists
             if not os.path.exists(self.extract_dir):
diff --git a/pooch/tests/test_processors.py b/pooch/tests/test_processors.py
index f00a2878..a378b71f 100644
--- a/pooch/tests/test_processors.py
+++ b/pooch/tests/test_processors.py
@@ -111,7 +111,7 @@ def test_extractprocessor_fails():
 
 
 @pytest.mark.parametrize(
-    "proc_cls,ext,dir",
+    "proc_cls,ext,_dir",
     [
         (Unzip, ".zip", None),
         (Untar, ".tar.gz", None),
@@ -122,7 +122,7 @@ def test_extractprocessor_fails():
 )
 def test_processors(proc_cls, ext, _dir):
     "Setup a hook and make sure it's only executed when downloading"
-    processor = proc_cls(members=["tiny-data.txt"])
+    processor = proc_cls(members=["tiny-data.txt"], extract_dir=_dir)
     suffix = proc_cls.suffix
     extract_dir = "tiny-data" + ext + suffix if _dir is None else _dir
     with TemporaryDirectory() as local_store: