diff --git a/test/test_networking.py b/test/test_networking.py
index 631e7458e6..f78a8d5770 100644
--- a/test/test_networking.py
+++ b/test/test_networking.py
@@ -755,6 +755,17 @@ class TestHTTPRequestHandler(TestRequestHandlerBase):
                 assert res.read(0) == b''
                 assert res.read() == b'<video src="/vid.mp4" /></html>'
 
+    def test_partial_read_greater_than_response_then_full_read(self, handler):
+        with handler() as rh:
+            for encoding in ('', 'gzip', 'deflate'):
+                res = validate_and_send(rh, Request(
+                    f'http://127.0.0.1:{self.http_port}/content-encoding',
+                    headers={'ytdl-encoding': encoding}))
+                assert res.headers.get('Content-Encoding') == encoding
+                assert res.read(512) == b'<html><video src="/vid.mp4" /></html>'
+                assert res.read(0) == b''
+                assert res.read() == b''
+
 
 @pytest.mark.parametrize('handler', ['Urllib', 'Requests', 'CurlCFFI'], indirect=True)
 @pytest.mark.handler_flaky('CurlCFFI', reason='segfaults')
@@ -920,6 +931,28 @@ class TestUrllibRequestHandler(TestRequestHandlerBase):
             assert res.fp.fp is None
             assert res.closed
 
+    def test_data_uri_partial_read_then_full_read(self, handler):
+        with handler() as rh:
+            res = validate_and_send(rh, Request('data:text/plain,hello%20world'))
+            assert res.read(6) == b'hello '
+            assert res.read(0) == b''
+            assert res.read() == b'world'
+            # Should automatically close the underlying file object
+            assert res.fp.closed
+            assert res.closed
+
+    def test_data_uri_partial_read_greater_than_response_then_full_read(self, handler):
+        with handler() as rh:
+            res = validate_and_send(rh, Request('data:text/plain,hello%20world'))
+            assert res.read(512) == b'hello world'
+            # Response and its underlying file object should already be closed now
+            assert res.fp.closed
+            assert res.closed
+            assert res.read(0) == b''
+            assert res.read() == b''
+            assert res.fp.closed
+            assert res.closed
+
     def test_http_error_returns_content(self, handler):
         # urllib HTTPError will try close the underlying response if reference to the HTTPError object is lost
         def get_response():
diff --git a/test/test_websockets.py b/test/test_websockets.py
index 637b6ee2b2..39b207d6b1 100644
--- a/test/test_websockets.py
+++ b/test/test_websockets.py
@@ -40,7 +40,7 @@ TEST_DIR = os.path.dirname(os.path.abspath(__file__))
 
 pytestmark = pytest.mark.handler_flaky(
     'Websockets',
-    os.name != 'nt' and sys.implementation.name == 'pypy',
+    os.name == 'nt' or sys.implementation.name == 'pypy',
     reason='segfaults',
 )
 
diff --git a/yt_dlp/networking/_urllib.py b/yt_dlp/networking/_urllib.py
index 34f2d45d3c..e3b4903456 100644
--- a/yt_dlp/networking/_urllib.py
+++ b/yt_dlp/networking/_urllib.py
@@ -305,6 +305,8 @@ class UrllibResponseAdapter(Response):
             status=getattr(res, 'status', None) or res.getcode(), reason=getattr(res, 'reason', None))
 
     def read(self, amt=None):
+        if self.closed:
+            return b''
         try:
             data = self.fp.read(amt)
             underlying = getattr(self.fp, 'fp', None)
