Fast MRI makes it possible to visualize dynamic biological phenomena and can potentially reduce the cost of diagnostic imaging. Constrained imaging methods such as compressive sense (CS) and optimal lattice sampling (OLS) have proven to be effective for speeding up MRI. In doing so, CS takes advantage of the image sparsity or compressibility and OLS utilizes the known signal/spectrum support. Interestingly, while CS requires sampling to be randomized to obtain incoherent artifacts which is critical for reconstruction, OLS mandates sampling to be on a structured lattice. In this paper, we proposed a method to integrate CS with OLS so that both the sparsity and support constraints can be used simultaneously. The method randomizes the sampling on the lattice and minimizes a convex cost function with sparsity constraint and data fidelity terms. Computer simulations in 3D MRI show that the proposed method allows greater accelerations with minimal degradation of the image quality.