We study epicyclic oscillations of fluid tori around black holes (in the Paczynski-Wiita potential) and derive exact analytic expressions for their radial and vertical eigenfrequencies to second-order accuracy in the width of the torus. We prove that pressure effects make the eigenfrequencies smaller than those for free particles. However,the particular ratio 3/2, which is important for the theory of high-frequency quasi-periodic oscillations (QPOs), occurs when the fluid tori epicyclic frequencies are about 15% higher than the ones corresponding to free particles. Our results therefore suggest that previous estimates of black hole spins from QPOs have produced values that are too high.