table unions - Mailing list pgsql-novice

Novice question:

How can I apply conditional logic when doing a union of two tables?

TableA                       TableB
------                      ------
value1  value2               value1  value2
   1      10                    5      15
  11      20

SELECT * FROM TableA UNION SELECT * FROM TableB;
returns:

value1  value2
   1      10
   5      15
  11      20


what I want is

value1  value2
   1       5
   5      15
  15      20

The tables are huge and already in ascending order.