Speckle limits the quantitative quality of SAR imagery and makes performing post-processing tasks difficult. It is therefore important to develop algorithms that can remove or minimise the influence of speckle while preserving the original data. In this paper we analyse the applicability of minimum cross-entropy methods for SAR image reconstruction. Our novel approach focuses on the form of the goodness-of-fit function for which we also employ an entropy function in addition to the penalty function. Such an approach seems more suited to the multiplicative nature of speckle. An adaptive minimum cross-entropy (MCE) algorithm is developed on this basis and its performance is investigated on both simulated and real SAR data. The results indicate a general level of performance comparable to commonly available reconstruction techniques such as those available in ENVI and CAESAR as well as a more traditional form of the entropy formulation. The method developed is found to be particularly well suited for images of natural landscapes containing a distribution of features and textures.