Previously, directed animals on the square and triangular lattices have been enumerated by area, and have been found to have simple generating functions, whilst the hexagonal lattice generating function has not been obtained. In this paper, directed animals on several new lattices are enumerated, one class of which is solved exactly. Directed animals by bonds (with and without loops) are also enumerated. In each case an asymptotic growth like n − 1 2 µ n is observed and precise estimates for µ are given.