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 V-r and V-z 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 V-z/V-r = 3/2, which is important for the theory of high-frequency quasi-periodic oscillations (QPOs), occurs when the fluid tori epicyclic frequencies V-r and V-z 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.