During the current rise phase of the Alcator A discharge a series of disruptions occurs, related to MHD activity of poloidal periodicity m, at limiter q-values approximately 1.6 m (m integral). The electron temperature profile is peaked at the centre throughout. It is shown, however, that current diffusion with the experimental Te profiles typically leads to hollow current profiles and that the disruptions appear to be related to the local minimum of q inside the plasma attaining near-integral values. Disruptions may be avoided by decreasing the rate of current rise. This leads to improved plasma conditions throughout the discharge.