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Parallel Imaging MRI (pMRI) and Compressive Sensing (CS) are two reconstruction techniques that have recently been applied to increase MRI performance. In this paper we demonstrate that a combined analysis of the pMRI and CS problems leads to a conceptually simple, yet effective technique that outperforms independent approaches to both reconstruction problems. We argue that the proposed technique is also naturally resilient to noise, due to its relation to the MAP image denoising formulation. A modified Basis Pursuit (BP) formulation of the CS-MRI problem allows it to handle the pMRI problem at the same time. We also present an exact solution to this BP problem, using the split Bregman technique, with discrete shearlet transform (DST) regularization. The DST is an excellent choice for natural image applications, due to its optimal sparsity property. Results show that this Compressive Parallel Sensing (COMPASS) reconstruction algorithm outperforms more traditional MRI reconstruction algorithms in both pMRI and CS experiments.