diff --git a/t/t5552-skipping-fetch-negotiator.sh b/t/t5552-skipping-fetch-negotiator.sh
index a452fe32fa..8f25f4b31f 100755
--- a/t/t5552-skipping-fetch-negotiator.sh
+++ b/t/t5552-skipping-fetch-negotiator.sh
@@ -173,7 +173,17 @@ test_expect_success 'do not send "have" with ancestors of commits that server AC
 	test_commit -C server commit-on-b1 &&
 
 	test_config -C client fetch.negotiationalgorithm skipping &&
-	trace_fetch client "$(pwd)/server" to_fetch &&
+
+	# NEEDSWORK: The number of "have"s sent depends on whether the transport
+	# is stateful. If the overspecification of the result were reduced, this
+	# test could be used for both stateful and stateless transports.
+	(
+		# Force protocol v0, in which local transport is stateful (in
+		# protocol v2 it is stateless).
+		GIT_TEST_PROTOCOL_VERSION=0 &&
+		export GIT_TEST_PROTOCOL_VERSION &&
+		trace_fetch client "$(pwd)/server" to_fetch
+	) &&
 	grep "  fetch" trace &&
 
 	# fetch-pack sends 2 requests each containing 16 "have" lines before