Efficient NoC is crucial for communication among processing elements in a highly parallel processing systems on chip. Mapping cores to slots in a NoC platform and designing efficient routing algorithms are two key problems in NoC design. Source routing offers major advantages over distributed routing especially for regular topology NoC platforms. But it suffers from a serious drawback of overhead since it requires whole communication path to be stored in every packet header. In this paper, we present a core mapping technique which helps to achieve a mapping with the constraint over the path length. We demonstrate the feasibility of reducing the path length to just 50% of the diameter. We also present a method to efficiently compute paths for source routing leading to good traffic distribution. Evaluation results show that performance degradation due to path length constraint is negligible at low as well at high communication traffic.