An approximate theory is presented which allows cross sections for rotational transitions in collisions between polar molecules to be estimated. The theory coverges to the time-dependent sudden approximation and to first-order perturbation theory in the appropriate limits; it can be regarded as an approximate form of the strong-coupling correspondence principle approximation. Unlike previous theories which have attempted to correct the sudden approximation for adiabatic effects, it treats rotational transitions of 'resonant' and 'non-resonant' type consistently. Its predictions are compared with close-coupling results for the system HF-HF.0022-3700/84/ 153135 + 15$02.25 0 1984 The Institute of Physics