Neutrino Factories and Muon Colliders require rapid acceleration of short-lived muons to multi-GeV and TeV energies. A Re-circulating Linear Accelerator (RLA) that uses a single Linac and teardrop return arcs can provide exceptionally fast and economical acceleration to the extent that the focusing range of the RLA quadrupoles allows each muon to pass several times through each high-gradient cavity and the cost of the return arcs is appropriate. Flexible Momentum Compaction (FMC) lattice designs for the teardrop return arcs provide sufficient momentum acceptance to allow multiple passes of each sign of muon in one string of magnets to improve cost-effectiveness.