We present new, high signal-to-noise ratio spectra of the core of M87. These data confirm Dressler's claim that the velocity dispersion does not continue to rise within r = 1 arcsec, but levels off at σ ∼ 360 km s-1. The line strength of the Mg b feature falls sharply in the nucleus due to the contribution of a nonthermal spectrum. The central light spike in M87 is completely explained by this non-thermal component, in contradiction to Dressler's (1980) claim that much of the spike is due to a central star cluster. Maximum entropy models have been constructed to match the new data. They exclude the possibility of a supermassive black hole M > 4 × l09 M⊙ unless a highly contrived model is accepted. A model with no supermassive black hole which has a mild anisotropy in the stellar orbits is a good fit to the data, but a model having only slightly greater anisotropy can accommodate a central mass concentration of up to 109 M⊙.