We consider Bayesian constraints on standard isocurvature baryon models from the slope and normalization of the anisotropy power spectrum detected by the COBE DMR experiment in their two year maps. In conjunction with either the amplitude of matter fluctuations \sigma_8 {\it or} its slope, all open models are ruled out at greater than 95\% confidence, whereas cosmological constant \Lambda dominated models are constrained to be highly ionized. By including the COBE FIRAS 95\% confidence upper limit on spectral distortion, we further reduce the available parameter space for \Lambda models by excluding these highly ionized models. These constraints define a single class of barely viable standard models which makes definite and testable predictions for degree scale anisotropies and large scale structure.
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