With DPCM, it is advantageous to adapt the quantizer characteristic to the signal. We have studied several schemes where a gain constant is controlled by either forward or backward estimation. With forward estimation, the gain is calculated on a two-dimensional block of data, and we have studied how the form and size of the block affects performance. With backward estimation, the Jayant algorithm has been extended from one to two dimensions by letting the change in gain constant depend upon prediction errors from neighboring elements on the present and previous line. Simulations are performed on a sequence of pictures from a monochrome videophone scene with very active movement. The improvement in mean square error with adaptive control is between 2 and 5 dB compared to the performance with a uniform fixed quantizer. The subjective improvement is substantial.