Narrowing is the operational principle of languages
that integrate functional and logic programming.
We propose a notion of a needed narrowing step that,
for inductively sequential rewrite systems,
extends the Huet and Levy notion of a needed reduction step.
We define a strategy, based on this notion,
that computes only needed narrowing steps.
Our strategy is sound and complete for a large class of rewrite systems,
is optimal w.r.t. the cost measure that
counts the number of distinct steps of a derivation,
computes only independent unifiers,
and is efficiently implemented by pattern matching.