  Ekpyrotic instantons describe the emergence of classical contracting
universes out of the no-boundary quantum state. However, up to now these
instantons ended in a big crunch singularity. We remedy this by adding a
higher-derivative term, allowing a ghost condensate to form. This causes a
smooth, non-singular bounce from the contracting phase into an expanding,
kinetic-dominated phase. Remarkably, and although there is a non-trivial
evolution during the bounce, the wavefunction of the universe is "classical" in
a WKB sense just as much after the bounce as before. These new non-singular
instantons can thus form the basis for a fully non-singular and calculable
ekpyrotic history of the universe, from creation until now.
