More than a dozen papers analyzing the COBE data have now appeared. We review the different techniques and compare them to a ``brute force" likelihood analysis where we invert the full 4038 x 4038 Galaxy-cut pixel covariance matrix. This method is optimal in the sense of producing minimal error bars, and is a useful reference point for comparing other analysis techniques. Our maximum-likelihood estimate of the spectral index and normalization are n=1.15 (0.95) and Q=18.2 (21.3) micro-Kelvin including (excluding) the quadrupole. Marginalizing over the normalization C_9, we obtain n=1.10 +/- 0.29 (n=0.90 +/- 0.32). When we compare these results with those of the various techniques that involve a linear ``compression'' of the data, we find that the latter are all consistent with the brute-force analysis and have error bars that are nearly as small as the minimal error bars. We therefore conclude that the data compressions involved in these techniques do indeed retain most of the useful cosmological information.