A comparison of the HOLD, CC and CC_KEPLER methods on integrating an unsoftened 1024-body Plummer sphere through core collapse: conservation of the integrals of motion (top two rows), evolution of the mass distribution of the solution (third row) and wall-clock time (bottom left). Lagrangian radii are plotted for 90%, 50%, 10% and 1% of the system mass. Wall-clock times are normalised by CC_KEPLER at the first global time step (1/64-th of the simulation). On a laptop with a 1.3 GHz Intel Core i5 processor, CC_KEPLER integrates the first global time step in roughly 5 min while the entire simulation takes about 7 h.