  We give a construction of the zero range and bricklayers' processes in the
totally asymmetric, attractive case. The novelty is that we allow jump rates to
grow exponentially. Earlier constructions have permitted at most linearly
growing rates. We also show the invariance and extremality of a natural family
of i.i.d. product measures indexed by particle density. Extremality is proved
with an approach that is simpler than existing ergodicity proofs.
