Spectrum-sliced elastic optical path networks (SLICE) enable flexible bandwidth provisioning, which allows efficient resource utilization and support to heterogeneous bandwidth demands. This makes SLICE a very promising networking architecture. In SLICE, finding a route and a slice of the spectrum is an important design problem, which is known as the Routing and Spectrum Assignment (RSA) problem. In this paper, we present a new heuristic, based on Yen's k-shortest path algorithm and capable of dealing with the traffic heterogeneity to find appropriate sets of paths for each source-destination node pairs to mitigate the bottleneck in the network. The results show that the proposed algorithm reduces the lightpath blocking probability and achieves significantly improved spectrum efficiency. We also analyse the maximum number of alternate shortest paths for minimising the blocking probability.