Small cell network (SCN) offers, for the first time, a low-cost and scalable mechanism to meet the forecast data-traffic demand. In this paper, we propose a non-uniform SCN deployment scheme. The small cell base stations (BSs) in this scheme will not be utilized in the region within a prescribed distance away from any macrocell BSs, defined as the inner region. Based upon the analytical framework provided in this work, the downlink coverage and single user throughput are precisely characterized. Provided that the inner region size is appropriately chosen, we find that the proposed non-uniform SCN deployment scheme can maintain the same level of cellular coverage performance even with 50% less small cell BSs used than the uniform SCN deployment, which is commonly considered in the literature. Furthermore, both the coverage and the single user throughput performance will significantly benefit from the proposed scheme, if its average small cell density is kept identical to the uniform SCN deployment. This work demonstrates the benefits obtained from a simple non-uniform SCN deployment, thus highlighting the importance of deploying small cells selectively.