The mapping of the fit of seismic moment tensor (MT) solutions in source-type space helps to characterize uncertainty and solution uniqueness. Current practice relies on the forward testing of a distribution of randomly generated MTs in source-type space, which is slow and does not necessarily recover the true maximum fit surface. We design an iterative damped least-squares inversion scheme to invert waveforms and/or P -wave first motions for best-fitting MT solutions for specific source types. An event associated with the sinkhole at the Napoleonville salt dome, Louisiana, an industrial quarry explosion, and an earthquake at The Geysers geothermal field, northern California, are presented as examples. We find that the inversion method is more accurate and successful than the random-search approach in recovering the region of best-fitting MT solutions or source types and is substantially faster. The approach also enables the determination of the best-fitting MT for specified source types such as pure double couples, tensile cracks, or explosions, as well as compound mechanisms in a single numerical framework. Online Material: Description and figures comparing inversion performance using spherical and Cartesian eigenvector parameterizations; figures showing the revised full moment tensor solution of event TE1 and additional network sensitivity solutions of event TE3.