  We consider largeness of groups given by a presentation of deficiency 1,
where the group is respectively free-by-cyclic, LERF or 1-relator. We give the
first examples of (finitely generated free)-by-(infinite cyclic) word
hyperbolic groups which are large, show that a LERF deficiency 1 group with
first Betti number at least 2 is large or the integers times the integers, and
show that 2-generator 1-relator groups where the relator has height 1 obey the
dichotomy that either the group is large or all its finite images are
metacyclic.
