diff --git a/src/h2/utilities.py b/src/h2/utilities.py
index c4e62f2f3..4a3ff823a 100644
--- a/src/h2/utilities.py
+++ b/src/h2/utilities.py
@@ -275,7 +275,7 @@ def _reject_empty_header_names(headers: Iterable[Header],
     """
     for header in headers:
         if len(header[0]) == 0:
-            msg = "Received header name with zero length."
+            msg = "Header name with zero length present."
             raise ProtocolError(msg)
         yield header
 
@@ -690,6 +690,9 @@ def validate_outbound_headers(headers: Iterable[Header],
     :param headers: The HTTP header set.
     :param hdr_validation_flags: An instance of HeaderValidationFlags.
     """
+    headers = _reject_empty_header_names(
+        headers, hdr_validation_flags,
+    )
     headers = _reject_te(
         headers, hdr_validation_flags,
     )
diff --git a/tests/test_invalid_headers.py b/tests/test_invalid_headers.py
index 2a68c6fc6..44daa07e8 100644
--- a/tests/test_invalid_headers.py
+++ b/tests/test_invalid_headers.py
@@ -672,6 +672,37 @@ def test_inbound_header_name_length(self, hdr_validation_flags) -> None:
         with pytest.raises(h2.exceptions.ProtocolError):
             list(h2.utilities.validate_headers([(b"", b"foobar")], hdr_validation_flags))
 
+    @pytest.mark.parametrize("hdr_validation_flags", hdr_validation_combos)
+    def test_outbound_header_name_length(self, hdr_validation_flags) -> None:
+        # An empty outbound header name must raise ProtocolError, not IndexError
+        # from the `header[0][0]` lookup in _reject_pseudo_header_fields.
+        with pytest.raises(h2.exceptions.ProtocolError):
+            list(h2.utilities.validate_outbound_headers([(b"", b"foobar")], hdr_validation_flags))
+
+    def test_outbound_header_name_length_send_headers(self, frame_factory) -> None:
+        c = h2.connection.H2Connection()
+        c.initiate_connection()
+        c.clear_outbound_data_buffer()
+
+        headers = [
+            (b":authority", b"example.com"),
+            (b":path", b"/"),
+            (b":scheme", b"https"),
+            (b":method", b"GET"),
+            (b"", b"foobar"),
+        ]
+        with pytest.raises(h2.exceptions.ProtocolError, match=r"Header name with zero length present\."):
+            c.send_headers(1, headers)
+
+    @pytest.mark.parametrize("hdr_validation_flags", [
+        flags for flags in hdr_validation_combos
+        if flags.is_trailer and not flags.is_response_header
+    ])
+    def test_valid_header_name_accepted_both_directions(self, hdr_validation_flags) -> None:
+        headers = [(b"x-custom-header", b"foobar")]
+        assert list(h2.utilities.validate_headers(list(headers), hdr_validation_flags))
+        assert list(h2.utilities.validate_outbound_headers(list(headers), hdr_validation_flags))
+
     def test_inbound_header_name_length_full_frame_decode(self, frame_factory) -> None:
         f = frame_factory.build_headers_frame([])
         f.data = b"\x00\x00\x01\x04"
@@ -682,7 +713,7 @@ def test_inbound_header_name_length_full_frame_decode(self, frame_factory) -> No
         c.receive_data(frame_factory.preamble())
         c.clear_outbound_data_buffer()
 
-        with pytest.raises(h2.exceptions.ProtocolError, match="Received header name with zero length."):
+        with pytest.raises(h2.exceptions.ProtocolError, match=r"Header name with zero length present\."):
             c.receive_data(data)