MadMonkey: That looks very wrong to me. The first tournament has only 8 players - there's shouldn't be any byes to begin with. The second tournament has 10 players - 6 players should have byes, the four remaining players should play the two matches in the first round. Ideally, the two matches should be distributed over both halves of the bracket; that is, if the winners of the first round matches keep winning, they should meet in the final.

If you use the schema below, and fill in the participants in order, then there will not be byes, and first round winners will meet as late as possible.

 1. ------+
          +------+
16. ------+      |
                 +------+
 8. ------+      |      |
          +------+      |
 9. ------+             |
                        |
                        +------+
                        |      |
 5. ------+             |      |
          +------+      |      |
12. ------+      |      |      |
                 +------+      |
 4. ------+      |             |
          +------+             |
13. ------+                    |
                               |
                               +-------
                               |
 3. ------+                    |
          +------+             |
14. ------+      |             |
                 +------+      |
 6. ------+      |      |      |
          +------+      |      |
11. ------+             |      |
                        |      |
                        +------+
                        |
 7. ------+             |
          +------+      |
10. ------+      |      |
                 +------+
 2. ------+      |
          +------+
15. ------+

This also easily generalizes to 32, 64, 128 participants (and to 8).