We present an approach to rewriting in inductively sequential
rewriting systems with a very distinctive feature.  In the class of
systems that we consider, any reducible term defines a needed step, a
step that must be executed by any rewriting computation that produces
the term's normal form.  We show an implementation of rewriting that
avoids executing some needed steps by replacing those steps with
function calls.  Our approach improves the efficiency of many
computations---in some cases by one or two orders of magnitude.  Our
work is motivated by and applicable to the implementation of
functional logic programming languages.