One of the key issues in providing end-to-end quality-of-service (QoS) guarantees in packet networks is how to determine a feasible path that satisยฎes a number of QoS constraints. For two or more additive constraints, the problem of ยฎnding a feasible path is NP-complete that cannot be exactly solved in polynomial time. Accordingly, several heuristics and approximation algorithms have been proposed for this problem. Many of these algorithms suffer from either excessive computational cost or low performance. In this paper, we provide an efยฎcient approximation algorithm for ยฎnding a path subject to two additive constraints. The worst-case computational complexity of this algorithm is within a logarithmic number of calls to Dijkstra's shortest path algorithm. Its average complexity is even much lower than that, as demonstrated by simulation experiments. The performance of the proposed algorithm is justiยฎed via theoretical bounds that are provided for the optimal version of the path selection problem. To achieve further performance improvement, several extensions to the basic algorithm are also provided at very low computational cost. Extensive simulations are used to demonstrate the high performance of the proposed algorithm and to contrast it with other path selection algorithms.