  Among (isotopy classes of) automorphisms of handlebodies those called
irreducible (or generic) are the most interesting, analogues of pseudo-Anosov
automorphisms of surfaces. We consider the problem of isotoping an irreducible
automorphism so that it is most efficient (has minimal growth rate) in its
isotopy class. We describe a property, called tightness, of certain invariant
laminations, which we conjecture characterizes this efficiency. We obtain
partial results towards proving the conjecture. For example, we prove it for
genus two handlebodies. We also show that tightness always implies efficiency.
In addition, partly in order to provide counterexamples in our study of
properties of invariant laminations, we develop a method for generating a class
of irreducible automorphisms of handlebodies.
