Conventional coupled modes are combined with perturbation theory to allow fast range-dependent normal mode calculations in deep water. The mode-coupling method follows R. B. Evan’s two-way coupled mode formulation [R. B. Evans, J. Acoust. Soc. Am. 74, 188–195 (1983)], where conservation of pressure and particle displacement along the z axis yields an algorithm to couple the modes as sound propagates in range. The conventional approach requires calculation of a complete set of normal modes at each step in range and is computationally intensive. Here perturbation theory is used to find the normal modes and wave numbers of each step in terms of linear combinations of the modes of the previous step. The process can be repeated for many steps and allows rapid calculation to long ranges. The method of coupled perturbed modes is applied to benchmark and canonical problems.