diff --git a/h11/_connection.py b/h11/_connection.py
index e37d82a..49eab15 100644
--- a/h11/_connection.py
+++ b/h11/_connection.py
@@ -478,8 +478,22 @@ def next_event(self) -> Union[Event, Type[NEED_DATA], Type[PAUSED]]:
         if self.their_state is ERROR:
             raise RemoteProtocolError("Can't receive data when peer state is ERROR")
         try:
+            # Snapshot length so we can measure how many bytes a completed
+            # header event consumed (request/response line + headers).
+            before = len(self._receive_buffer)
             event = self._extract_next_receive_event()
             if event not in [NEED_DATA, PAUSED]:
+                # Enforce max_incomplete_event_size for completed header events
+                # too (python-hyper/h11#182). Oversized headers that arrive in
+                # one chunk previously parsed successfully, while the same
+                # bytes split across packets hit the NEED_DATA size check —
+                # making enforcement depend on TCP framing.
+                if isinstance(event, (Request, InformationalResponse, Response)):
+                    consumed = before - len(self._receive_buffer)
+                    if consumed > self._max_incomplete_event_size:
+                        raise RemoteProtocolError(
+                            "Receive buffer too long", error_status_hint=431
+                        )
                 self._process_event(self.their_role, cast(Event, event))
             if event is NEED_DATA:
                 if len(self._receive_buffer) > self._max_incomplete_event_size:
diff --git a/h11/tests/test_connection.py b/h11/tests/test_connection.py
index 01260dc..4d496b0 100644
--- a/h11/tests/test_connection.py
+++ b/h11/tests/test_connection.py
@@ -486,6 +486,16 @@ def test_max_incomplete_event_size_countermeasure() -> None:
         c.next_event()
 
 
+    # Complete oversized headers in a single chunk must also be rejected
+    # (previously only incomplete buffers above the limit were checked).
+    oversized = b"GET / HTTP/1.0\r\nBig: " + b"a" * 200 + b"\r\n\r\n"
+    assert len(oversized) > 100
+    c = Connection(SERVER, max_incomplete_event_size=100)
+    c.receive_data(oversized)
+    with pytest.raises(RemoteProtocolError):
+        c.next_event()
+
+
 def test_reuse_simple() -> None:
     p = ConnectionPair()
     p.send(