diff --git a/test.py b/test.py
index 8184c17..17e605a 100644
--- a/test.py
+++ b/test.py
@@ -660,7 +660,7 @@ def stream(self, method, url, params, headers):
 
     def test_too_many_bytes(self):
         @contextmanager
-        def server():
+        def server(port):
             def _run(server_sock):
                 while True:
                     try:
@@ -671,12 +671,12 @@ def _run(server_sock):
                     connection_t.start()
 
             with shutdown(get_new_socket()) as server_sock:
-                server_sock.bind(('127.0.0.1', 9001))
+                server_sock.bind(('127.0.0.1', port))
                 server_sock.listen(socket.IPPROTO_TCP)
                 threading.Thread(target=_run, args=(server_sock,)).start()
                 yield server_sock
 
-        def get_http_client():
+        def get_http_client(port):
             @contextmanager
             def client():
                 with httpx.Client() as original_client:
@@ -684,9 +684,9 @@ class Client():
                         @contextmanager
                         def stream(self, method, url, params, headers):
                             parsed_url = urllib.parse.urlparse(url)
-                            url = urllib.parse.urlunparse(parsed_url._replace(netloc='localhost:9001'))
+                            url = urllib.parse.urlunparse(parsed_url._replace(netloc=f'localhost:{port}'))
                             range_query = dict(headers).get('range')
-                            is_query = range_query and range_query != 'bytes=0-99'
+                            yield_extra = not only_after_header or (range_query and range_query != 'bytes=0-99')
                             headers_proxy_host = tuple((key, value) for key, value in headers if key != 'host') + (('host', 'localhost:9000'),)
                             with original_client.stream(method, url,
                                 params=params, headers=headers_proxy_host
@@ -694,29 +694,31 @@ def stream(self, method, url, params, headers):
                                 chunks = response.iter_bytes()
                                 def iter_bytes(chunk_size=None):
                                     yield from chunks
-                                    if is_query:
+                                    if yield_extra:
                                         yield b'e'
                                 response.iter_bytes = iter_bytes
                                 yield response
                     yield Client()
             return client()
 
-        with server() as server_sock:
-            with get_db([
-                ("CREATE TABLE my_table (my_col_a text, my_col_b text);",()),
-            ] + [
-                ("INSERT INTO my_table VALUES " + ','.join(["('some-text-a', 'some-text-b')"] * 500),()),
-            ]) as db:
-                put_object_with_versioning('my-bucket', 'my.db', db)
-
-            with sqlite_s3_query('http://localhost:9000/my-bucket/my.db', get_credentials=lambda now: (
-                'us-east-1',
-                'AKIAIOSFODNN7EXAMPLE',
-                'wJalrXUtnFEMI/K7MDENG/bPxRfiCYEXAMPLEKEY',
-                None,
-            ), get_http_client=get_http_client, get_libsqlite3=get_libsqlite3) as query:
-                with self.assertRaisesRegex(SQLiteError, 'disk I/O error'):
-                    query('SELECT my_col_a FROM my_table').__enter__()
+        for only_after_header, port in [(False, 9001), (True, 9002)]:
+            with self.subTest((only_after_header, port)):
+                with server(port) as server_sock:
+                    with get_db([
+                        ("CREATE TABLE my_table (my_col_a text, my_col_b text);",()),
+                    ] + [
+                        ("INSERT INTO my_table VALUES " + ','.join(["('some-text-a', 'some-text-b')"] * 500),()),
+                    ]) as db:
+                        put_object_with_versioning('my-bucket', 'my.db', db)
+
+                    with sqlite_s3_query('http://localhost:9000/my-bucket/my.db', get_credentials=lambda now: (
+                        'us-east-1',
+                        'AKIAIOSFODNN7EXAMPLE',
+                        'wJalrXUtnFEMI/K7MDENG/bPxRfiCYEXAMPLEKEY',
+                        None,
+                    ), get_http_client=functools.partial(get_http_client, port), get_libsqlite3=get_libsqlite3) as query:
+                        with self.assertRaisesRegex(SQLiteError, 'disk I/O error'):
+                            query('SELECT my_col_a FROM my_table').__enter__()
 
     def test_disconnection(self):
         @contextmanager
@@ -732,7 +734,7 @@ def _run(server_sock):
                     connection_t.start()
 
             with shutdown(get_new_socket()) as server_sock:
-                server_sock.bind(('127.0.0.1', 9001))
+                server_sock.bind(('127.0.0.1', 9003))
                 server_sock.listen(socket.IPPROTO_TCP)
                 threading.Thread(target=_run, args=(server_sock,)).start()
                 yield server_sock
@@ -744,7 +746,7 @@ def client():
                     class Client():
                         def stream(self, method, url, headers, params):
                             parsed_url = urllib.parse.urlparse(url)
-                            url = urllib.parse.urlunparse(parsed_url._replace(netloc='localhost:9001'))
+                            url = urllib.parse.urlunparse(parsed_url._replace(netloc='localhost:9003'))
                             headers_proxy_host = tuple((key, value) for key, value in headers if key != 'host') + (('host', 'localhost:9000'),)
                             return original_client.stream(method, url, headers=headers_proxy_host)
                     yield Client()