Implications of a Small CP Asymmetry in B->psi K_S

New measurements of the CP asymmetry in B->\psi K_S, a_{\psi K_S}, by the BABAR and BELLE collaborations are consistent with the Standard Model prediction for sin2\beta. These measurements, however, leave open the possibility that a_{\psi K_S} is well below the Standard Model prediction. We identify deviations from the `reasonable ranges' of hadronic parameters that can lead to low values of sin2\beta. New physics, mainly in B^0-\barB^0 mixing and/or K^0-\barK^0 mixing, can explain low values of a_{\psi K_S} in two ways: either by allowing for values of sin2\beta below the Standard Model prediction or by modifying the relation between a_{\psi K_S} and sin2\beta.