Upper ocean baroclinic instability has been recently studied in a ``reduced gravity'' setting, by means of a quasigeostrophic 21/2-layer model on the b-plane. This approximation is formally valid when the total ocean depth tends to infinity. The effect of a finite ocean depth is examined here using a 3-layer model. The basic state is a zonal current with uniform velocities within each layer. The ratio e between the sum of the upper two layers mean depths and the lower layer mean depth is the relevant new parameter of the problem. Even for very small values of e, important differences between the 21/2-layer e =0) and the 3-layer model are found. As e increases the region of Arnold stable states decreases. For certain basic states new normal mode instability branches are found, whose growth rates increase with e. An asymptotic expansion in e is made in order to shed some light on the transition regime between both models. This allows to interpret the new instabilities as a consequence of the resonant interplay between the stable modes in the 21/2-layer model and a short Rossby wave in the deep layer. The growth rates of the new instability branches are O(e1/3) and O(e1/2), and cannot be neglected even for reasonably small values of e.