  Hybrid symplectic integrators such as MERCURY are widely used to simulate
complex dynamical phenomena in planetary dynamics that could otherwise not be
investigated. A hybrid integrator achieves high accuracy during close
encounters by using a high order integration scheme for the duration of the
encounter while otherwise using a standard 2nd order Wisdom-Holman scheme,
thereby optimizing both speed and accuracy. In this paper we reassess the
criteria for choosing the switching function that determines which parts of the
Hamiltonian are integrated with the high order integrator. We show that the
original motivation for choosing a polynomial switching function in MERCURY is
not correct. We explain the nevertheless excellent performance of the MERCURY
integrator and then explore a wide range of different switching functions
including an infinitely differentiable function and a Heaviside function. We
find that using a Heaviside function leads to a significantly simpler scheme
compared to MERCURY, while maintaining the same accuracy in short term
simulations.
