Velocity-space tomography provides a way of diagnosing fast ions in a fusion plasma by combining measurements from multiple instruments. We use a toroidally viewing and a vertically viewing fast-ion D-alpha (FIDA) diagnostic installed on the spherical tokamak MAST (before the upgrade) to perform velocity-space tomography of the fast-ion distribution function. To make up for the scarce amount of data, prior information is included in the inversions. We impose a non-negativity constraint, suppress the distribution in the velocity-space region associated with null-measurements, and encode the belief that it does not extend to energies significantly higher than those expected neoclassically. This allows us to study the fast-ion velocity distributions and the derived fast-ion densities before and after a sawtooth crash.