We present a new approach to the execution of functional logic
programs. Our approach relies on definitional trees for the
deterministic portions of a computation and on a graph
transformation, called pull-tab, for the non-deterministic
portions.  This transformation moves, one level at a time,
non-deterministic choices towards the root of the graph
representing the state of a computation.  With respect to
need-based strategies for functional logic computations, our
approach executes only localized graph replacements, a property
that characterizes it as ``pay as you go'' and makes it suitable
for parallel execution.