  We study two types of generalized Baxter-Wu models, by means of
transfer-matrix and Monte Carlo techniques. The first generalization allows for
different couplings in the up- and down triangles, and the second
generalization is to a $q$-state spin model with three-spin interactions. Both
generalizations lead to self-dual models, so that the probable locations of the
phase transitions follow. Our numerical analysis confirms that phase
transitions occur at the self-dual points. For both generalizations of the
Baxter-Wu model, the phase transitions appear to be discontinuous.
