Largeness of LERF and 1-relator groups

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 thefirst examples of (finitely generated free)-by-(infinite cyclic) wordhyperbolic groups which are large, show that a LERF deficiency 1 group withfirst Betti number at least 2 is large or the integers times the integers, andshow that 2-generator 1-relator groups where the relator has height 1 obey thedichotomy that either the group is large or all its finite images aremetacyclic.