Consider a road network, and let the preferred subnet consist of the roads a driver is more acquainted to and hence tends to follow. In this paper, we study the problem of finding the most preferred path between two network nodes; we consider two variants of this problem. We first target the Most Preferred Unrestricted Path (MPUP) that has the lowest traveling time in the non-preferred subnet; this problem was introduced in the literature as identifying the safest path though safe zones. As MPUP imposes no constraints on the total traveling time, we then introduce the Most Preferred Near Shortest Path (MPNSP) that has the lowest traveling time in the non-preferred subnet among all paths which are not much slower than the shortest path. We focus on the efficient evaluation of both problems by proposing solutions with simple pre-processing steps. An extensive evaluation demonstrates the efficiency of our techniques compared to the existing method for MPUP and to the state-of-the-art on computing multi-criteria shortest paths for MPNSP. CCS CONCEPTS • Information systems → Spatial-temporal systems;