The absorption of an ultra-intense circularly-polarized laser pulse by a near-critical (0.1nc < ne < a0nc) plasma is studied. Previously two regimes of absorption have been suggested: a 'leading edge depletion' (LED) regime and a 'transverse ponderomotive acceleration' regime. Here we seek to describe these concepts more thoroughly, and determine if two distinct regimes actually exist. New analytic models to describe each regime are derived. These are compared with 1D and 2D particle-in-cell simulations, and good quantitative agreement is found, showing the existence of two separate regimes. The LED regime exhibits very efficient absorption of laser light, which is promising for applications.