  We consider the minimal model program for varieties that are not Q-factorial.
We show that, in many cases, its steps are simpler than expected. In
particular, all flips are 1-complemented. The main applications are to log
terminal singularities, removing the earlier Q-factoriality assumption from
several theorems of Hacon--Witaszek and de~Fernex--Koll\'ar--Xu. Version 2:
many small changes.
