We propose a new distributed QoS routing scheme called pre-computation based selective probing (PCSP). The PCSP scheme is designed to provide an exact solution to the constrained optimization problem with moderate overhead, considering the practical environment where the state information available for the routing decision is not exact. It does not limit the number of probe messages, instead, employs a qualitative (or conditional) selective probing approach. It considers both the cost and QoS metrics of the least-cost and the best-QoS paths to calculate the end-to-end cost of the found feasible paths and find QoS-satisfying least-cost paths. It defines strict probing condition that excludes not only the non-feasible paths but also the non-optimal paths. It additionally pre-computes the QoS variation taking into account the impreciseness of the state information and applies two modified QoS-satisfying conditions to the selection rules. This strict probing condition and carefully designed probing approaches enable to strictly limit the set of neighbor nodes involved in the probing process, thereby reducing the message overhead without sacrificing the optimal properties. However, the PCSP scheme may suffer from high message overhead due to its conservative search process in the worst case. In order to bound such message overhead, we extend the PCSP algorithm by applying additional quantitative heuristics. Computer simulations reveal that the PCSP scheme reduces message overhead and possesses ideal success ratio with guaranteed optimal search. In addition, the quantitative extensions of the PCSP scheme turn out to bound the worst-case message overhead with slight performance degradation.