diff --git a/builtin/describe.c b/builtin/describe.c
index b6df81d..420f4c6 100644
--- a/builtin/describe.c
+++ b/builtin/describe.c
@@ -376,11 +376,25 @@
 			if (!(c->object.flags & t->flag_within))
 				t->depth++;
 		}
+		/* Stop if last remaining path already covered by best candidate(s) */
 		if (annotated_cnt && !list) {
-			if (debug)
-				fprintf(stderr, _("finished search at %s\n"),
-					oid_to_hex(&c->object.oid));
-			break;
+			int best_depth = INT_MAX;
+			unsigned best_within = 0;
+			for (cur_match = 0; cur_match < match_cnt; cur_match++) {
+				struct possible_tag *t = &all_matches[cur_match];
+				if (t->depth < best_depth) {
+					best_depth = t->depth;
+					best_within = t->flag_within;
+				} else if (t->depth == best_depth) {
+					best_within |= t->flag_within;
+				}
+			}
+			if ((c->object.flags & best_within) == best_within) {
+				if (debug)
+					fprintf(stderr, _("finished search at %s\n"),
+						oid_to_hex(&c->object.oid));
+				break;
+			}
 		}
 		while (parents) {
 			struct commit *p = parents->item;
diff --git a/t/t6120-describe.sh b/t/t6120-describe.sh
index 09c50f3..34502e3 100755
--- a/t/t6120-describe.sh
+++ b/t/t6120-describe.sh
@@ -479,4 +479,55 @@
 	)
 '
 
+#               B
+#               o
+#                \
+#  o-----o---o----x
+#        A
+#
+test_expect_success 'describe commits with disjoint bases' '
+	git init disjoint1 &&
+	(
+		cd disjoint1 &&
+
+		echo o >> file && git add file && git commit -m o &&
+		echo A >> file && git add file && git commit -m A &&
+		git tag A -a -m A &&
+		echo o >> file && git add file && git commit -m o &&
+
+		git checkout --orphan branch && rm file &&
+		echo B > file2 && git add file2 && git commit -m B &&
+		git tag B -a -m B &&
+		git merge --no-ff --allow-unrelated-histories master -m x &&
+
+		check_describe "A-3-*" HEAD
+	)
+'
+
+#           B
+#   o---o---o------------.
+#                         \
+#                  o---o---x
+#                  A
+#
+test_expect_success 'describe commits with disjoint bases 2' '
+	git init disjoint2 &&
+	(
+		cd disjoint2 &&
+
+		echo A >> file && git add file && GIT_COMMITTER_DATE="2020-01-01 18:00" git commit -m A &&
+		git tag A -a -m A &&
+		echo o >> file && git add file && GIT_COMMITTER_DATE="2020-01-01 18:01" git commit -m o &&
+
+		git checkout --orphan branch &&
+		echo o >> file2 && git add file2 && GIT_COMMITTER_DATE="2020-01-01 15:00" git commit -m o &&
+		echo o >> file2 && git add file2 && GIT_COMMITTER_DATE="2020-01-01 15:01" git commit -m o &&
+		echo B >> file2 && git add file2 && GIT_COMMITTER_DATE="2020-01-01 15:02" git commit -m B &&
+		git tag B -a -m B &&
+		git merge --no-ff --allow-unrelated-histories master -m x &&
+
+		check_describe "B-3-*" HEAD
+	)
+'
+
 test_done