We show that, under appropriate oblique-incidence and polarization conditions, the inherent opaqueness of a homogeneous, isotropic single-negative slab may be perfectly compensated (in the ideal lossless case) by a homogeneous, anisotropic (uniaxial) double-positive slab, so that complete tunneling (with total transmission and zero phase delay) occurs. We present an analytical and numerical study aimed at deriving the basic design rules, elucidating the underlying physical mechanisms, and exploring the role of the various involved parameters.