Direct constructions for balanced tournaments known so far solve problems with 2n teams if 2n mod 3 not equal 1 or 2n = 2(p), p >= 3 or n is odd. Our construction uses an arbitrary partition of the league into subleagues. It solves more than half of the missing cases and provides structured solutions for some known cases. (C) 2007 Elsevier B.V. All rights reserved.