Regularizing time transformations in symplectic and composite integration

We consider numerical integration of nearly integrable Hamiltonian systems. The emphasis is on perturbed Keplerian motion, such as certain cases of the problem of two fixed centres and the restricted three-body problem. We show that the presently known methods have useful generalizations which are explicit and have a variable physical timestep which adjusts to both the central and perturbing potentials. These methods make it possible to compute accurately fairly close encounters. In some cases we suggest the use of composite (instead of symplectic) alternatives which typically seem to have equally good energy conservation properties.