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#104
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Double-elimination Olympic system, for 8 participants, for simplicity let's assume the first numbers listed in each pair win:

Round 1
1->5
2->6
3->7
4->8

Round 2
1->3
2->4

5->7
6->8
7, 8 - lost twice and are eliminated

Round 3
1->2

3->5
4->6
5, 6 - lost twice and are eliminated

Round 4
1->4 (since they already played against #3)

2->3
3, 4 - lost twice and are eliminated

Final
1->2 for the tournament win

3->4 for third place

More details http://ru.wikipedia.org/wiki/Олимпийская_система_с_выбыванием_после_двух_поражений
PS I prefer a simple Olympic system.