The results of direct numerical simulations of convection in a uniformly rotating vertical cylinder with no-slip boundary conditions are described, and used to study the dynamics associated with transitions between states with adjacent azimuthal wave numbers far from onset. In certain regimes a novel burst-like state is identified and described. A dynamical-systems explanation for this behavior is suggested. © 2003 Published by The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved.