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Heuristic QoS algorithms under strict constraints perform poorly in terms of finding a path that is suitable for a user's QoS needs-the multiple constraint path problem (MCP). Exact QoS algorithms, on the other hand, guarantee that a path satisfying user needs would be found and offer a more realistic approach for solving the MCP problem in view of the fact that the NP-complete character of graphs are not common in real networks. This fact has driven approaches like the SAMCRA and A*prune algorithms. However, these algorithms still have very high running times relative to heuristic approaches. When QoS routing algorithms are used in online traffic engineering (TE) environments it may be necessary to route thousands of traffic flows each minute. Exact algorithms simply cannot work in such environments. We propose a heuristic algorithm that is suitable for working in an online TE environment. Simulations show that this algorithm produce high success rates in terms of finding suitable constraint paths for user flows while at the same time having execution times comparable to another heuristic based algorithms.