diff --git a/mysql-test/r/group_min_max.result b/mysql-test/r/group_min_max.result
index 9d1c495eb27..9421ea9e740 100644
--- a/mysql-test/r/group_min_max.result
+++ b/mysql-test/r/group_min_max.result
@@ -2129,10 +2129,11 @@ Warnings:
 Note	1003	select sum(ord(`test`.`t1`.`a1`)) AS `sum(ord(a1))` from `test`.`t1` where (`test`.`t1`.`a1` > 'a') group by `test`.`t1`.`a1`,`test`.`t1`.`a2`,`test`.`t1`.`b`
 create table t4 as select distinct a1, a2, b, c from t1;
 alter table t4 add unique index idxt4 (a1, a2, b, c);
+# This is "superceded" by MDEV-7118, and Loose Index Scan is again an option:
 explain
 select a1, a2, b, min(c) from t4 group by a1, a2, b;
 id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
-1	SIMPLE	t4	index	NULL	idxt4	163	NULL	64	Using index
+1	SIMPLE	t4	range	NULL	idxt4	147	NULL	10	Using index for group-by
 select a1, a2, b, min(c) from t4 group by a1, a2, b;
 a1	a2	b	min(c)
 a	a	a	a111
@@ -2355,7 +2356,7 @@ CREATE TABLE t2 (a int, b int, c int, PRIMARY KEY (a,b,c));
 INSERT INTO t2 SELECT a,b,b FROM t1;
 explain SELECT MIN(c) FROM t2 WHERE b = 2 and a = 1 and c > 1 GROUP BY a;
 id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
-1	SIMPLE	t2	ref	PRIMARY	PRIMARY	8	const,const	1	Using where; Using index
+1	SIMPLE	t2	range	PRIMARY	PRIMARY	12	NULL	1	Using where; Using index for group-by
 SELECT MIN(c) FROM t2 WHERE b = 2 and a = 1 and c > 1 GROUP BY a;
 MIN(c)
 2
diff --git a/mysql-test/r/group_min_max_innodb.result b/mysql-test/r/group_min_max_innodb.result
index f3511b0ad4a..77c74fbc041 100644
--- a/mysql-test/r/group_min_max_innodb.result
+++ b/mysql-test/r/group_min_max_innodb.result
@@ -174,7 +174,7 @@ F	17
 EXPLAIN SELECT c1, max(i2) FROM t1 WHERE (c1 = 'C' OR c1 = 'F' ) AND ( i2 = 17 )
 GROUP BY c1;
 id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
-1	SIMPLE	t1	range	k1	k1	5	NULL	2	Using where; Using index
+1	SIMPLE	t1	range	k1	k1	5	NULL	1	Using where; Using index for group-by
 SELECT c1, max(i2) FROM t1 WHERE (c1 = 'C' OR c1 = 'F' ) AND ( i2 = 17 )
 GROUP BY c1;
 c1	max(i2)
diff --git a/mysql-test/t/group_min_max.test b/mysql-test/t/group_min_max.test
index f58350013be..8c9be0ca8db 100644
--- a/mysql-test/t/group_min_max.test
+++ b/mysql-test/t/group_min_max.test
@@ -704,6 +704,7 @@ explain extended select sum(ord(a1)) from t1 where (a1 > 'a') group by a1,a2,b;
 create table t4 as select distinct a1, a2, b, c from t1;
 alter table t4 add unique index idxt4 (a1, a2, b, c);
 
+--echo # This is "superceded" by MDEV-7118, and Loose Index Scan is again an option:
 explain
 select a1, a2, b, min(c) from t4 group by a1, a2, b;
 select a1, a2, b, min(c) from t4 group by a1, a2, b;
diff --git a/sql/opt_range.cc b/sql/opt_range.cc
index dec104c3903..a5c27fa66e2 100644
--- a/sql/opt_range.cc
+++ b/sql/opt_range.cc
@@ -12801,11 +12801,11 @@ get_best_group_min_max(PARAM *param, SEL_TREE *tree, double read_time)
     uint cur_used_key_parts;
     
     /*
-      Check (B1) - if current index is covering. Exclude UNIQUE indexes, because
-      loose scan may still be chosen for them due to imperfect cost calculations.
+      Check (B1) - if current index is covering.
+      (was also: "Exclude UNIQUE indexes ..." but this was removed because 
+      there are cases Loose Scan over a multi-part index is useful).
     */
-    if (!table->covering_keys.is_set(cur_index) ||
-        cur_index_info->flags & HA_NOSAME)
+    if (!table->covering_keys.is_set(cur_index))
       goto next_index;
 
     /*
@@ -12943,6 +12943,16 @@ get_best_group_min_max(PARAM *param, SEL_TREE *tree, double read_time)
       min_max_arg_part= cur_index_info->key_part + key_part_nr - 1;
     }
 
+    /*
+      Aplly a heuristic: there is no point to use loose index scan when we're
+      using the whole unique index.
+    */
+    if (cur_index_info->flags & HA_NOSAME && 
+        cur_group_key_parts == cur_index_info->user_defined_key_parts)
+    {
+      goto next_index;
+    }
+
     /*
       Check (NGA1, NGA2) and extract a sequence of constants to be used as part
       of all search keys.