We consider the problem of designing an adaptive receiver with anM-bit memory for binary orthogonal signaling over a slowly fading Rayleigh channel. Both the cases of decision-feedback and no decision-feedback are considered. We present a problem formulation by defining the contents of the receiver's memory. The structure of the Bayes receiver that makes optimum use of the memory information is then established. The LRT that defines the receiver is obtained explicitly, and it dictates a detector-estimator receiver structure. The detector can be interpreted as being partially coherent, with coherence being achieved asymptotically in the limit of perfect estimation of the fading process. Simulation results are given to show the improved error rate performance of the adaptive receiver. Our results also indicate that decision-feedback should be employed in a manner dependent on the SNR.