There are two known general results on the finite model property (fmp) of commutators [L0, L1] (bimodal logics with commuting and confluent modalities). If L is finitely axiomatisable by modal formulas having universal Horn first-order correspondents, then both [L,K] and [L,S5] are determined by classes of frames that admit filtration, and so have the fmp. On the negative side, if both L0 and L...