In this paper, we study a bandwidth allocation strategy with state-dependent Bernoulli access (SDBA) and preemptive priority (PP) to serve wideband (WB) and narrowband (NB) traffics in wideband integrated networks. In this strategy, total bandwidth is divided into three regions, bandwidth for WB traffic, bandwidth for NB traffic and shared bandwidth. Under this environment, the minimum usable bandwidths for queueable NB traffic are controlled adaptively according to the system states. And the bandwidths used by the NB traffic are probabilistically preempted by a blockable WB traffic, when the number of NB messages waiting in the buffer is varying. The strategy is analyzed using the Neuts' matrix analytic approach. It shows better performance than other schemes which do not use SDBA and PP. In addition, the strategy with multiple buffer thresholds controls bandwidth allocation more dynamically and shows more performance build-up than the strategy with single buffer threshold.