  We consider minimal-perimeter lattice animals, providing a set of conditions
which are sufficient for a lattice to have the property that inflating all
minimal-perimeter animals of a certain size yields (without repetitions) all
minimal-perimeter animals of a new, larger size. We demonstrate this result on
the two-dimensional square and hexagonal lattices. In addition, we characterize
the sizes of minimal-perimeter animals on these lattices that are not created
by inflating members of another set of minimal-perimeter animals.
