Table lookup with interpolation is used for many learning and adaptation tasks. Redundant mappings capture the important concept of "motor skill," which is important in real, behaving systems. Few robot skill implementations have dealt with redundant mappings, in which the space to be searched to create the table has much higher dimensionality than the table. A practical method for inverting redundant mappings is important in physical systems with limited time for trials. We present the "Guided table Fill In" algorithm, which uses data already stored in the table to guide search through the space of potential table entries. The algorithm is illustrated and tested on a robot skill learning task both in simulation and on a robot with a flexible link. Our experiments show that the ability to search high dimensional action spaces efficiently allows skill learners to find new behaviors that are qualitatively different from what they were presented or what the system designer may have expected. Thus the use of this technique can allow researchers to seek higher dimensional action spaces for their systems rather than constraining their search space at the risk of excluding the best actions.