Most existing work in designing sensing matrices for compressive recovery is based on optimizing some quality factor, such as mutual coherence, average coherence or the restricted isometry constant (RIC), of the sensing matrix. In this paper, we report anomalous results that show that such a design is not always guaranteed to improve reconstruction results. We also present a design method based on the minimum mean squared error (MMSE) criterion, imposing priors on signal and noise for natural images, and show that it yields results superior to results from coherence-based methods while taking into account physical constraints on the sensing matrix.