Using three elements of the Navy Prototype Optical Interferometer and observing in 20 spectral channels covering 520-850 nm, we have implemented a phase bootstrapping technique in which short baselines with high visibilities are used to keep the longer baselines with low visibilities in phase. Using this method, we have been able to extend the spatial frequency coverage beyond the first zero of the stellar visibility function for two K giants α Arietis, and α Cassiopeiae. The data are inconsistent with a uniform-disk model and confirm the presence of limb-darkened radial profiles. Adopting a particular limb-darkening law enables us to determine the diameter with small formal errors (one part in 1000). In addition, we have measured closure phases for both stars. The closure phases show a jump of 180° at the first zero in the visibility amplitude, which was expected.