We consider Rayleigh-Bénard convection inside slim rectangular cells of transversal aspect ratio Γ. In such configurations, a change of regime is observed as the depth becomes comparable to the size of thermal plumes, going from an unconfined regime I, to a plume-controlled regime II, and to a confined regime III. For the latter, we developed a reduced model, which improves the Hele-Shaw approximation by taking into account inertial corrections terms. This is done in the spirit of similar work inside Hele-Shaw cells by [Gondret and Rabaud (1997)], then extended by [Ruyer-Quil, (2001)]. The reduced model is validated against 3D DNS results. We take advantage of the lower computational cost of the model to perform a parametric study for different (Ra,Pr) in the range 1/256 < Γ < 1/32. We identify a new, severely confined regime, noted IV, and compare it to theoretical predictions. This transition is related to changes in flow structure, as well as in the relative thickness of thermal and viscous boundary layers.