The evolution of the ratio between P- and S-wave velocities (V-P/V-S) with increasing fluid-saturated porosity is computed for isotropic rocks containing spheroidal pores. The ratio V-P/V-S is shown to either decrease or increase with increasing porosity, depending on the aspect ratio alpha of the pores, fluid to solid bulk modulus ratio zeta and Poisson's ratio nu(0) of the solid constituents of the rock. A critical initial Poisson's ratio nu(0, crit) is computed, separating cases where V-P/V-S increases (if nu(0) < nu(0), (crit)) or decreases (if nu(0) > nu(0, crit)) with increasing porosity. For thin cracks and highly compressible fluids, nu(0), (crit) is approximated by 0.157 zeta/alpha, whereas for spherical pores nu(0, crit) is given by 0.2 + 0.8 zeta. When nu(0) is close to nu(0, crit), the evolution of V-P/V-S with increasing fluid-saturated porosity is near neutral and depends on subtle changes in pore shape and fluid properties. This regime is found to be relevant to partially dehydrated serpentinites in subduction zones (porosity of aspect ratio near 0.1 and. in the range 0.01-0.1), and makes detection of these rocks and possibly elevated fluid pressures difficult from V-P/V-S only.