We present HEJ 2, a new implementation of the High Energy Jets formalism for high-energy resummation in hadron-collider processes as a flexible Monte Carlo event generator. In combination with a conventional fixed-order event generator, HEJ 2 can be used to obtain greatly improved predictions for a number of phenomenologically important processes by adding all-order logarithmic corrections in s / p^2. A prime example for such a process is the gluon-fusion production of a Higgs boson in association with widely separated jets, which constitutes the dominant background to Higgs boson production in weak-boson fusion.