Are SP91 and COBE Inconsistent with Cold Dark Matter?

We present results on the consistency of standard cold dark matter (CDM) models with both the COBE normalization and the data from the 4th channel of the 9-point South Pole scan. We find that CDM models are consistent with both experiments, a conclusion which is at odds with some other analyses. This is partly due to our careful treatment of the temperature autocorrelation function, but also derives from a realization that the statistical conclusions depend strongly on assumptions about the prior distribution for the normalization $Q$.