We apply a Wiener filter to the two-year COBE DMR data. The resulting sky map has significantly reduced noise levels compared to the raw data: the most prominent hot and cold spots are significant at the 4-sigma level. Furthermore, the entire covariance matrix of the errors in the filtered sky map is known, and it is therefore possible to make constrained realizations of the microwave sky with the correct a posteriori probability distribution. The filtered DMR sky map is used to make predictions for the Tenerife experiment. Two prominent features are predicted in a region of the sky not yet analyzed by the Tenerife group. The presence of these features is a robust prediction of the standard cosmological paradigm; if these features are not observed, some of our fundamental assumptions must be incorrect.