While there is some confusion on this subject, scheduling byes are determined by the total number of teams in the the league. Having multiple divisions rather than one, does not in itself result in byes. In fact, multiple divisions help reduce the total number byes.
To prevent byes completely we can, depending on the number of teams,
- Limit the total number of teams
- or Have different number of teams in each division. One division would play friendlies in the last two weeks
- or Increase the number of divisions
For example
25 teams - Do not allow, exclude one team
26 teams - Division 1 14 teams, Division 2 12 teams27 teams - Do not allow, exclude one team
28 teams - Two divisions 14 teams in each division29 teams - Do not allow, exclude one team
30 teams - Three divisions 10 teams in each division
The team to be excluded would be the Last In First Out (LIFO)