Efforts to model sunspots based on helioseismic signatures need to discriminate between the effects of (1) a strong magnetic field that introduces time-irreversible, vantage-dependent phase shifts, apparently connected to fast- and slow-mode coupling and wave absorption and (2) a thermal anomaly that includes cool gas extending an indefinite depth beneath the photosphere. Helioseismic observations of sunspots show travel times considerably reduced with respect to equivalent quiet-Sun signatures. Simulations by Moradi Cally of waves skipping across sunspots with photospheric magnetic fields of order 3 kG show travel times that respond strongly to the magnetic field and relatively weakly to the thermal anomaly by itself. We note that waves propagating vertically in a vertical magnetic field are relatively insensitive to the magnetic field, while remaining highly responsive to the attendant thermal anomaly. Travel-time measurements for waves with large skip distances into the centers of axially symmetric sunspots are therefore a crucial resource for discrimination of the thermal anomaly beneath sunspot umbrae from the magnetic anomaly. One-dimensional models of sunspot umbrae based on compressible-radiative-magnetic-convective simulations such as by Rempel et al. can be fashioned to fit observed helioseismic travel-time spectra in the centers of sunspot umbrae. These models are based on cooling of the upper 2-4 Mm of the umbral subphotosphere with no significant anomaly beneath 4.5 Mm. The travel-time reductions characteristic of these models are primarily a consequence of a Wilson depression resulting from a strong downward buoyancy of the cooled umbral medium.