Analytical models of plasma sheaths provide physical insight and are useful in 2-d and 3-d plasma simulations, where numerical solution of the sheath equations at each boundary point is too time-consuming to be practical. Analytical models have long been known for the high-frequency and low-frequency limits, where the time it takes ions to cross the sheath, ti, is either much greater than or much less than the rf period, T. At intermediate frequencies, where ti ≈ T, sheath behavior is more complicated. In addition to the well-known narrowing of ion energy distributions (IEDs) there are other, lesser known effects at ti ≈ T, including changes in the ion current — which becomes strongly time-dependent within the sheath — and in IED peak intensities, average ion energy, sheath impedance, and sheath power. Existing analytical models of collisionless sheaths based on the "damped potential" formalism yield accurate predictions for IED widths and peak energies, but not for any of the other phenomena. Here, we describe a different approach for modeling intermediate-frequency, collisionless sheaths. It captures the essential elements of ion dynamics yet still provides analytical expressions for most sheath properties. Others require minimal numerical effort, such as a single numerical integration of an analytical expression. Predictions of the analytical model are compared to previous analytical results, complete numerical solutions of the relevant partial differential equations, and, where possible, experimental data. The model yields new insights into ion dynamics and may serve to increase the accuracy of 2-d and 3-d plasma simulations, in particular, their predictions for power and average ion energy.