We investigate the dynamics of bubble rearrangements in coarsening foams, using a time-resolved multiple light scattering technique. We measure the average duration of such events as a function of the foam confinement pressure. Rearrangements slow down as the pressure is decreased toward the jamming point. Our results are explained by a scaling law based on the balance of pressure and Darcy flow, highlighting an analogy between wet foams with mobile interfaces and suspensions of hard grains.