diff --git a/builtin/fetch.c b/builtin/fetch.c
index 6ab101fa6d..c26866e674 100644
--- a/builtin/fetch.c
+++ b/builtin/fetch.c
@@ -1782,11 +1782,10 @@ static int do_fetch(struct transport *transport,
 			    "refs/tags/");
 	}
 
-	if (uses_remote_tracking(transport, rs)) {
-		must_list_refs = 1;
+	if (must_list_refs &&
+	    uses_remote_tracking(transport, rs))
 		strvec_push(&transport_ls_refs_options.ref_prefixes,
 			    "HEAD");
-	}
 
 	if (must_list_refs) {
 		trace2_region_enter("fetch", "remote_refs", the_repository);
diff --git a/t/t5702-protocol-v2.sh b/t/t5702-protocol-v2.sh
index 626deb05f0..4d0cbe9872 100755
--- a/t/t5702-protocol-v2.sh
+++ b/t/t5702-protocol-v2.sh
@@ -708,6 +708,19 @@ test_expect_success 'exact oid fetch with tag following' '
 	git -C exact-oid-tags rev-parse --verify my-tag
 '
 
+test_expect_success 'exact oid fetch avoids pointless HEAD request' '
+	git init exact-oid-head &&
+	git -C exact-oid-head remote add origin ../prefix-parent &&
+
+	commit=$(git -C prefix-parent rev-parse --verify HEAD) &&
+
+	test_when_finished "rm -f log" &&
+	GIT_TRACE_PACKET="$(pwd)/log" \
+		git -C exact-oid-head fetch --no-tags origin \
+			$commit:refs/heads/exact &&
+	test_grep ! command=ls-refs log
+'
+
 test_expect_success 'fetch supports various ways of have lines' '
 	rm -rf server client trace &&
 	git init server &&