Model-based compressive sensing (CS) exploits the structure inherent in sparse signals for the design of better signal recovery algorithms. This information about structure is often captured in the form of a prior on the sparse coefficients, with the Laplacian being the most common such choice (leading to l₁-norm minimization). Recent work has exploited the discriminative capability of sparse representations for image classification by employing class-specific dictionaries in the CS framework. Our contribution is a logical extension of these ideas into structured sparsity for classification. We introduce the notion of discriminative class-specific priors in conjunction with class specific dictionaries, specifically the spike-and-slab prior widely applied in Bayesian sparse regression. Significantly, the proposed framework takes the burden off the demand for abundant training image samples necessary for the success of sparsity-based classification schemes. We demonstrate this practical benefit of our approach in important applications, such as face recognition and object categorization.