In this paper, we propose a novel compressive sensing scheme for sparse signals with non-uniform sparsity. The proposed scheme integrates direct sampling and compressive sensing. In many real-life sparse signals, the significant coefficients of the signal are non-uniformly distributed along the signal vector. This non-uniformity in sparsity can be employed as additional information to improve the quality of signal recovery. Some recovery algorithms employ the signal sparsity model to enhance the compressive sensing performance. These algorithms generally incorporate the extra information with the recovery algorithm. In this paper, we propose to exploit the extra information to deliberately employ the direct sampling for the dense parts of a signal vector. We analytically find the conditions that the proposed method outperforms conventional compressive sensing. We also provide numerical simulations to support our findings.