We examine various algorithms for calculating quality of service (QoS)-enabled paths spanning multiple autonomous systems (ASs) using the path computation element (PCE) architecture. The problem is divided into two parts. We first calculate an AS path, then the node-by-node path. Using extensive simulation, we compared various AS-path calculation algorithms based on border gateway protocol (BGP) and various AS-aggregation procedures, such as mesh, star and nodal aggregation. For node-to-node path calculation, we employed the per-domain backward algorithm and the per-domain backward tree algorithm (also known as backward recursive PCE-based computation). Results point to the fact that complex AS-path calculation algorithms do not perform significantly better than BGP. However, if the service quality provided by ASs varies greatly, either in time or space, then we expect a QoS-aware AS-path computation algorithm, e.g., static nodal aggregation, to outperform BGP. Although the per-domain backward tree algorithm generally performs better than the per-domain backward algorithm, using a persistent variant of the latter makes it outperform the per-domain backward tree algorithm. The cost is a negligible increase in computational complexity and a slightly increased connection setup delay.