We consider threshold-based admission control policies for traffic in fixed-route circuit-switched networks, and develop a scheme for adjusting the threshold parameters online so that, as operating conditions in the network change, the thresholds "adapt" with the objective of minimizing a weighted sum of call blocking probabilities. Instrumental in this scheme is an algorithm for estimating online the sensitivity of the call blocking metric with respect to thresholds. The formal optimization problem over the set of discrete threshold parameters is solved by means of a conversion to an optimization problem over a set of auxiliary real-valued parameters. Such threshold-based policies, though conservative at low traffic rates, have the advantage of being simple to implement, distributed in nature, adaptive, and not requiring explicit distributional modeling assumptions. Numerical results included in the paper indicate that at higher traffic rates these simple policies yield the some performance as more complex and less flexible call admission schemes.