The Courant–Friedrichs–Lewy (CFL) condition is a well known, necessary condition for the stability of explicit time-stepping schemes that effectively places a limit on the size of the largest admittable time-step for a given problem. We formulate and present a new local time-stepping (LTS) scheme optimized, in the CFL sense, for the shallow water equations (SWEs). This new scheme, called FB-LTS, is based on the CFL optimized forward-backward Runge-Kutta schemes from Lilly et al. We show that FB-LTS maintains exact conservation of mass and absolute vorticity when applied to the TRiSK spatial discretization, and provide numerical experiments showing that it retains the temporal order of the scheme on which it is based (second order). We implement FB-LTS, along with a certain operator splitting, in MPAS-Ocean to test computational performance. This scheme, SplitFB-LTS, is up to 10 times faster than the classical four-stage, fourth-order Runge-Kutta method (RK4), and 2.3 times faster than an existing strong stability preserving Runge-Kutta based LTS scheme with the same operator splitting (SplitLTS3). Despite this significant increase in efficiency, the solutions produced by SplitFB-LTS are qualitatively equivalent to those produced by both RK4 and SplitLTS3.