Power ultrasound are known to enhance crystals nucleation, and nucleation times can be reduced by one up to three orders of magnitude for several organic or inorganic crystals. The precise mechanism of this phenomenon is yet unclear, but various theoretical explanations involve the action of inertial cavitation bubbles: cooling effect, pressure effect, segregation effect and evaporation effect. All these effects sound reasonable and may in fact act in a complementary fashion. The pressure effect is mediated by the high pressures appearing near the bubble as the latter collapses. The increase in pressure shifts the thermodynamical equilibrium. Zinc sulphate (ZnSO 4 .7H 2 O) has the interesting property that its solubility is not sensitive to pressure. We therefore carried out experiments of ZnSO 4 .7H 2 O crystallization by cooling in a 0.5 L crystallizer, both under silent conditions and by 20 W/cm 2 insonification with a horn transducer. The induction time is found almost independent of supersaturation under ultrasound, and much lower than the one obtained in silent conditions for low supersaturation (0.021 g of ZnSO 4 .7H 2 O / g solution). These experimental results question the generality of the pressure effect.