diff --git a/mysql-test/r/func_group.result b/mysql-test/r/func_group.result
index 896b79297f8..f0fd489867d 100644
--- a/mysql-test/r/func_group.result
+++ b/mysql-test/r/func_group.result
@@ -821,6 +821,144 @@ SELECT MAX(id) FROM t1 WHERE id < 3 AND a=2 AND b=6;
 MAX(id)
 NULL
 DROP TABLE t1;
+create table t1m (a int) engine=myisam;
+create table t1i (a int) engine=innodb;
+create table t2m (a int) engine=myisam;
+create table t2i (a int) engine=innodb;
+insert into t2m values (5);
+insert into t2i values (5);
+select min(a) from t1m;
+min(a)
+NULL
+select min(7) from t1m;
+min(7)
+NULL
+select min(7) from DUAL;
+min(7)
+NULL
+explain select min(7) from t2m join t1m;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	NULL	NULL	NULL	NULL	NULL	NULL	NULL	Select tables optimized away
+select min(7) from t2m join t1m;
+min(7)
+NULL
+select max(a) from t1m;
+max(a)
+NULL
+select max(7) from t1m;
+max(7)
+NULL
+select max(7) from DUAL;
+max(7)
+NULL
+explain select max(7) from t2m join t1m;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	NULL	NULL	NULL	NULL	NULL	NULL	NULL	Select tables optimized away
+select max(7) from t2m join t1m;
+max(7)
+NULL
+select 1, min(a) from t1m where a=99;
+1	min(a)
+1	NULL
+select 1, min(a) from t1m where 1=99;
+1	min(a)
+1	NULL
+select 1, min(1) from t1m where a=99;
+1	min(1)
+1	NULL
+select 1, min(1) from t1m where 1=99;
+1	min(1)
+1	NULL
+select 1, max(a) from t1m where a=99;
+1	max(a)
+1	NULL
+select 1, max(a) from t1m where 1=99;
+1	max(a)
+1	NULL
+select 1, max(1) from t1m where a=99;
+1	max(1)
+1	NULL
+select 1, max(1) from t1m where 1=99;
+1	max(1)
+1	NULL
+select min(a) from t1i;
+min(a)
+NULL
+select min(7) from t1i;
+min(7)
+NULL
+select min(7) from DUAL;
+min(7)
+NULL
+explain select min(7) from t2i join t1i;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	t2i	ALL	NULL	NULL	NULL	NULL	1	
+1	SIMPLE	t1i	ALL	NULL	NULL	NULL	NULL	1	
+select min(7) from t2i join t1i;
+min(7)
+NULL
+select max(a) from t1i;
+max(a)
+NULL
+select max(7) from t1i;
+max(7)
+NULL
+select max(7) from DUAL;
+max(7)
+NULL
+explain select max(7) from t2i join t1i;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	t2i	ALL	NULL	NULL	NULL	NULL	1	
+1	SIMPLE	t1i	ALL	NULL	NULL	NULL	NULL	1	
+select max(7) from t2i join t1i;
+max(7)
+NULL
+select 1, min(a) from t1i where a=99;
+1	min(a)
+1	NULL
+select 1, min(a) from t1i where 1=99;
+1	min(a)
+1	NULL
+select 1, min(1) from t1i where a=99;
+1	min(1)
+1	NULL
+select 1, min(1) from t1i where 1=99;
+1	min(1)
+1	NULL
+select 1, max(a) from t1i where a=99;
+1	max(a)
+1	NULL
+select 1, max(a) from t1i where 1=99;
+1	max(a)
+1	NULL
+select 1, max(1) from t1i where a=99;
+1	max(1)
+1	NULL
+select 1, max(1) from t1i where 1=99;
+1	max(1)
+1	NULL
+explain select count(*), min(7), max(7) from t1m, t1i;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	t1m	system	NULL	NULL	NULL	NULL	0	const row not found
+1	SIMPLE	t1i	ALL	NULL	NULL	NULL	NULL	1	
+select count(*), min(7), max(7) from t1m, t1i;
+count(*)	min(7)	max(7)
+0	NULL	NULL
+explain select count(*), min(7), max(7) from t1m, t2i;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	t1m	system	NULL	NULL	NULL	NULL	0	const row not found
+1	SIMPLE	t2i	ALL	NULL	NULL	NULL	NULL	1	
+select count(*), min(7), max(7) from t1m, t2i;
+count(*)	min(7)	max(7)
+0	NULL	NULL
+explain select count(*), min(7), max(7) from t2m, t1i;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	t2m	system	NULL	NULL	NULL	NULL	1	
+1	SIMPLE	t1i	ALL	NULL	NULL	NULL	NULL	1	
+select count(*), min(7), max(7) from t2m, t1i;
+count(*)	min(7)	max(7)
+0	NULL	NULL
+drop table t1m, t1i, t2m, t2i;
 CREATE TABLE t1 (id int PRIMARY KEY, b char(3), INDEX(b));
 INSERT INTO t1 VALUES (1,'xx'), (2,'aa');
 SELECT * FROM t1;
diff --git a/mysql-test/r/select.result b/mysql-test/r/select.result
index 32c9fabb19e..3df4f3f78ec 100644
--- a/mysql-test/r/select.result
+++ b/mysql-test/r/select.result
@@ -3151,6 +3151,55 @@ select count(*)
 from t1 inner join (t2 right join t3 on t2.id = t3.b_id) on t1.id = t3.a_id;
 count(*)
 6
+CREATE TABLE t1 (key1 float default NULL, UNIQUE KEY key1 (key1));
+CREATE TABLE t2 (key2 float default NULL, UNIQUE KEY key2 (key2));
+INSERT INTO t1 VALUES (0.3762),(0.3845),(0.6158),(0.7941);
+INSERT INTO t2 VALUES (1.3762),(1.3845),(1.6158),(1.7941);
+explain select max(key1) from t1 where key1 <= 0.6158;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	NULL	NULL	NULL	NULL	NULL	NULL	NULL	Select tables optimized away
+explain select max(key2) from t2 where key2 <= 1.6158;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	NULL	NULL	NULL	NULL	NULL	NULL	NULL	Select tables optimized away
+explain select min(key1) from t1 where key1 >= 0.3762;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	NULL	NULL	NULL	NULL	NULL	NULL	NULL	Select tables optimized away
+explain select min(key2) from t2 where key2 >= 1.3762;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	NULL	NULL	NULL	NULL	NULL	NULL	NULL	Select tables optimized away
+explain select max(key1), min(key2) from t1, t2
+where key1 <= 0.6158 and key2 >= 1.3762;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	NULL	NULL	NULL	NULL	NULL	NULL	NULL	Select tables optimized away
+explain select max(key1) from t1 where key1 <= 0.6158 and rand() + 0.5 >= 0.5;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	NULL	NULL	NULL	NULL	NULL	NULL	NULL	Select tables optimized away
+explain select min(key1) from t1 where key1 >= 0.3762 and rand() + 0.5 >= 0.5;
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	SIMPLE	NULL	NULL	NULL	NULL	NULL	NULL	NULL	Select tables optimized away
+select max(key1) from t1 where key1 <= 0.6158;
+max(key1)
+0.61580002307892
+select max(key2) from t2 where key2 <= 1.6158;
+max(key2)
+1.6158000230789
+select min(key1) from t1 where key1 >= 0.3762;
+min(key1)
+0.37619999051094
+select min(key2) from t2 where key2 >= 1.3762;
+min(key2)
+1.3761999607086
+select max(key1), min(key2) from t1, t2
+where key1 <= 0.6158 and key2 >= 1.3762;
+max(key1)	min(key2)
+0.61580002307892	1.3761999607086
+select max(key1) from t1 where key1 <= 0.6158 and rand() + 0.5 >= 0.5;
+max(key1)
+0.61580002307892
+select min(key1) from t1 where key1 >= 0.3762 and rand() + 0.5 >= 0.5;
+min(key1)
+0.37619999051094
+DROP TABLE t1,t2;
 drop table t1,t2,t3;
 create table t1 (a int);
 create table t2 (b int);
diff --git a/mysql-test/t/select.test b/mysql-test/t/select.test
index a55645bcc7c..197d89d02d5 100644
--- a/mysql-test/t/select.test
+++ b/mysql-test/t/select.test
@@ -2319,6 +2319,36 @@ SELECT STRAIGHT_JOIN SQL_NO_CACHE * FROM t2, t1 WHERE t1.b = t2.b OR t2.b IS NUL
 EXPLAIN SELECT STRAIGHT_JOIN SQL_NO_CACHE COUNT(*) FROM t2, t1 WHERE t1.b = t2.b OR t2.b IS NULL;
 SELECT STRAIGHT_JOIN SQL_NO_CACHE * FROM t2, t1 WHERE t1.b = t2.b OR t2.b IS NULL;
 DROP TABLE IF EXISTS t1,t2;
+#
+# Bug #20954 "avg(keyval) retuns 0.38 but max(keyval) returns an empty set"
+#
+--disable_ps_protocol
+CREATE TABLE t1 (key1 float default NULL, UNIQUE KEY key1 (key1));
+CREATE TABLE t2 (key2 float default NULL, UNIQUE KEY key2 (key2));
+INSERT INTO t1 VALUES (0.3762),(0.3845),(0.6158),(0.7941);
+INSERT INTO t2 VALUES (1.3762),(1.3845),(1.6158),(1.7941);
+
+explain select max(key1) from t1 where key1 <= 0.6158;
+explain select max(key2) from t2 where key2 <= 1.6158;
+explain select min(key1) from t1 where key1 >= 0.3762;
+explain select min(key2) from t2 where key2 >= 1.3762;
+explain select max(key1), min(key2) from t1, t2
+where key1 <= 0.6158 and key2 >= 1.3762;
+explain select max(key1) from t1 where key1 <= 0.6158 and rand() + 0.5 >= 0.5;
+explain select min(key1) from t1 where key1 >= 0.3762 and rand() + 0.5 >= 0.5;
+
+select max(key1) from t1 where key1 <= 0.6158;
+select max(key2) from t2 where key2 <= 1.6158;
+select min(key1) from t1 where key1 >= 0.3762;
+select min(key2) from t2 where key2 >= 1.3762;
+select max(key1), min(key2) from t1, t2
+where key1 <= 0.6158 and key2 >= 1.3762;
+select max(key1) from t1 where key1 <= 0.6158 and rand() + 0.5 >= 0.5;
+select min(key1) from t1 where key1 >= 0.3762 and rand() + 0.5 >= 0.5;
+
+DROP TABLE t1,t2;
+--enable_ps_protocol
+
 # End of 4.1 tests
 
 #
diff --git a/sql/sql_select.cc b/sql/sql_select.cc
index 93b0201b8f5..f6f45aea41e 100644
--- a/sql/sql_select.cc
+++ b/sql/sql_select.cc
@@ -679,6 +679,24 @@ JOIN::optimize()
       DBUG_PRINT("info",("Select tables optimized away"));
       zero_result_cause= "Select tables optimized away";
       tables_list= 0;				// All tables resolved
+      /*
+        Extract all table-independent conditions and replace the WHERE
+        clause with them. All other conditions were computed by opt_sum_query
+        and the MIN/MAX/COUNT function(s) have been replaced by constants,
+        so there is no need to compute the whole WHERE clause again.
+        Notice that make_cond_for_table() will always succeed to remove all
+        computed conditions, because opt_sum_query() is applicable only to
+        conjunctions.
+      */
+      if (conds)
+      {
+        COND *table_independent_conds=
+          make_cond_for_table(conds, PSEUDO_TABLE_BITS, 0);
+        DBUG_EXECUTE("where",
+                     print_where(table_independent_conds,
+                                 "where after opt_sum_query()"););
+        conds= table_independent_conds;
+      }
     }
   }
   if (!tables_list)