diff --git a/refs.c b/refs.c
index 20ba82b434..2ca715d099 100644
--- a/refs.c
+++ b/refs.c
@@ -487,16 +487,24 @@ static const char *ref_rev_parse_rules[] = {
 	NULL
 };
 
+#define NUM_REV_PARSE_RULES (ARRAY_SIZE(ref_rev_parse_rules) - 1)
+
+/*
+ * Is it possible that the caller meant full_name with abbrev_name?
+ * If so return a non-zero value to signal "yes"; the magnitude of
+ * the returned value gives the precedence used for disambiguation.
+ *
+ * If abbrev_name cannot mean full_name, return 0.
+ */
 int refname_match(const char *abbrev_name, const char *full_name)
 {
 	const char **p;
 	const int abbrev_name_len = strlen(abbrev_name);
+	const int num_rules = NUM_REV_PARSE_RULES;
 
-	for (p = ref_rev_parse_rules; *p; p++) {
-		if (!strcmp(full_name, mkpath(*p, abbrev_name_len, abbrev_name))) {
-			return 1;
-		}
-	}
+	for (p = ref_rev_parse_rules; *p; p++)
+		if (!strcmp(full_name, mkpath(*p, abbrev_name_len, abbrev_name)))
+			return &ref_rev_parse_rules[num_rules] - p;
 
 	return 0;
 }
diff --git a/remote.c b/remote.c
index c10d87c246..4a3e7ba136 100644
--- a/remote.c
+++ b/remote.c
@@ -1880,11 +1880,18 @@ static struct ref *get_expanded_map(const struct ref *remote_refs,
 static const struct ref *find_ref_by_name_abbrev(const struct ref *refs, const char *name)
 {
 	const struct ref *ref;
+	const struct ref *best_match = NULL;
+	int best_score = 0;
+
 	for (ref = refs; ref; ref = ref->next) {
-		if (refname_match(name, ref->name))
-			return ref;
+		int score = refname_match(name, ref->name);
+
+		if (best_score < score) {
+			best_match = ref;
+			best_score = score;
+		}
 	}
-	return NULL;
+	return best_match;
 }
 
 struct ref *get_remote_ref(const struct ref *remote_refs, const char *name)
diff --git a/t/t5510-fetch.sh b/t/t5510-fetch.sh
index da9ac00557..858381a788 100755
--- a/t/t5510-fetch.sh
+++ b/t/t5510-fetch.sh
@@ -535,6 +535,41 @@ test_expect_success "should be able to fetch with duplicate refspecs" '
 	)
 '
 
+test_expect_success 'LHS of refspec follows ref disambiguation rules' '
+	mkdir lhs-ambiguous &&
+	(
+		cd lhs-ambiguous &&
+		git init server &&
+		test_commit -C server unwanted &&
+		test_commit -C server wanted &&
+
+		git init client &&
+
+		# Check a name coming after "refs" alphabetically ...
+		git -C server update-ref refs/heads/s wanted &&
+		git -C server update-ref refs/heads/refs/heads/s unwanted &&
+		git -C client fetch ../server +refs/heads/s:refs/heads/checkthis &&
+		git -C server rev-parse wanted >expect &&
+		git -C client rev-parse checkthis >actual &&
+		test_cmp expect actual &&
+
+		# ... and one before.
+		git -C server update-ref refs/heads/q wanted &&
+		git -C server update-ref refs/heads/refs/heads/q unwanted &&
+		git -C client fetch ../server +refs/heads/q:refs/heads/checkthis &&
+		git -C server rev-parse wanted >expect &&
+		git -C client rev-parse checkthis >actual &&
+		test_cmp expect actual &&
+
+		# Tags are preferred over branches like refs/{heads,tags}/*
+		git -C server update-ref refs/tags/t wanted &&
+		git -C server update-ref refs/heads/t unwanted &&
+		git -C client fetch ../server +t:refs/heads/checkthis &&
+		git -C server rev-parse wanted >expect &&
+		git -C client rev-parse checkthis >actual
+	)
+'
+
 # configured prune tests
 
 set_config_tristate () {