  Given any generating set of any pseudo-Anosov-containing subgroup of the
mapping class group of a surface, we construct a pseudo-Anosov with word length
bounded by a constant depending only on the surface. More generally, in any
subgroup G we find an element f with the property that the minimal subsurface
supporting a power of f is as large as possible for elements of G; the same
constant bounds the word length of f. Along the way we find new examples of
convex cocompact free subgroups of the mapping class group.
