  We consider a class of partially hyperbolic diffeomorphisms introduced in
[BFP] which is open and closed and contains all known examples. If in addition
the diffeomorphism is non-wandering, then we show it is accessible unless it
contains a su-torus. This implies that these systems are ergodic when they
preserve volume, confirming a conjecture by Hertz-Hertz-Ures for this class of
systems.
