We extend our previous research on the instability properties of the laminar incompressible flow of density &rgr; and viscosity μ, which develops behind a cylindrical body with a rounded nose and length-to-diameter ratio L/D = 2, aligned with a free-stream of velocity w∞ [E. Sanmiguel-Rojas &etal;, Phys. Fluids 21, 114102 (2009); P. Bohorquez &etal;, J. Fluid Mech. 676, 110 (2011)]. In particular, we analyze the effects of a cylindrical base cavity of length h and diameter Dc on both critical Reynolds number, Rec = &rgr;w∞D/μ, and drag coefficient, CD, combining experiments, three-dimensional direct numerical simulations, and global linear stability analyses. The direct numerical simulations and the global stability results predict with precision the stabilizing effect of the cavity on the stationary, three-dimensional bifurcation in the wake as h/D increases. In fact, it is shown that, for a given value of Dc/D, the critical Reynolds number for the steady bifurcation, Recs, increases monotonically as h/D increases, reaching an asymptotic value which depends on Dc/D, at h/D ≈ 0.7. Likewise, for a fixed value of h/D, we have studied the effect of the cavity diameter Dc/D on the critical Reynolds number. No effect on Recs is observed over the range 0≤Dc/D≲0.6, but Recs shows a monotonic growth for 0.6≲Dc/Drsim0.5 and Dc/D ↠ 1. Similar behavior with the cavity length has been observed experimentally and numerically for the second, oscillatory bifurcation, and its associated critical Reynolds number, Reco.