The airline fleet assignment problem (FAP) consists of assigning an aircraft type to each flight leg of a flight schedule in order to maximize the airline expected profit. Most existing fleet assignment models (FAMs) use an estimation of the revenues per flight leg that neglects the interdependency between the flight legs and poorly approximates the spill and recapture of the passengers. To overcome this difficulty, Dumas et al. (2009) have introduced an iterative solution method for the FAP that solves at each iteration a FAM and a passenger flow model (PFM). A solution to the PFM provides the expected number of passengers on each leg, taking into account spill and recapture. These numbers are then used to better estimate the revenues per flight leg for the next iteration. Compared to solving a FAM once, this method yields better quality solutions but requires much larger computational times. In this paper, we aim at reducing these computational times while preserving solution quality. To do so, we propose to reevaluate periodically the flight leg revenues via the PFM while solving the FAM with a heuristic branch-and-bound algorithm. Computational results obtained for a large-scale real-life network and various demand levels show that the proposed method achieves this goal.