  We show that a locally finite variety which omits abelian types is
self-regulating if and only if it has a compatible semilattice term operation.
Such varieties must have a type-set {5}. These varieties are residually small
and, when they are finitely generated, they have definable principal
congruences. We show that idempotent varieties with a compatible semilattice
term operation have the congruence extension property.
