We investigate the impact of two strategies for dynamic pickup and delivery problems on the quality of solutions produced by insertion heuristics: (a) a waiting strategy that delays the final assignment of vehicles to their next destination, and (b) a request buffering strategy that postpones the assignment of some non-urgent new requests to the next route planning. In this study, the strategies are tested in a constructive-deconstructive heuristic for the dynamic pickup and delivery problem with hard time windows and random travel times. Comparisons of the solution quality provided by these strategies to a more conventional approach were performed on randomly generated instances up to 100 requests with static and dynamic (time-dependent) travel times and different degrees of dynamism. The results indicate the advantages of the strategies both in terms of lost requests and number of vehicles.