Band fusion modifies a link by fusing together two components of the link with a band. The effects of fusion on link invariants has been studied and the fusion pathways between links have been tabulated. We extended this work with an analysis of the effects of strong fusion, a modified form of fusion that preserves the number of components of a link by introducing an unknotted component around the fusion band. In particular, we determine the exact effect of strong fusion on several link invariants including the Alexander polynomial, Jones polynomial, and their generalization of the HOMFLY polynomial. We determine values for which of these polynomials remain unchanged by strong fusion. We also studied the Q-polynomial, signature, and the xi invariant. The work on the orientation independent invariants, the Q-polynomial and the xi invariant, is original; the effect of strong fusion on signature and HOMFLY has been studied by Kaiser (’91), but we extend and compliment his results. We also used link invariants⁠—including knottedness, linking number, and the dichromatic invariants of J. Hoste and M. Kidwell⁠—to classify which links are the result of strong fusion, tabulating all such links with up to 9 crossings.