In this paper, we propose selective estimation of least square based predictor algorithm and efficient overhead management scheme for lossless compression of digital mammograms. We exploit the characteristics of mammograms that most of the mammograms contain large number of blocks with constant gray level pixels, so a block based selective least square estimation algorithm is proposed. In our proposed algorithm if all the pixels have same intensity value in any block, then we represents those blocks by a single ('1') bit otherwise the block is decorrelated using the feed forward type of autoregressive modeling. We exploit the relationship between autoregression parameters which saves around 25% overhead burden. We have also empirically found that the AR parameters of the neighboring blocks are highly correlated and to get the best decorrelation among these parameters, median edge detector (MED) is used which gives us around 40% more saving in overhead burden. So, our proposed lossless compression algorithm for digital mammograms gives better entropy and minimum overhead burden then most of the algorithms reported in literature. ©2010 IEEE.