  Starting from trace formulae for the tunnelling splittings (or decay rates)
analytically continued in the complex time domain, we obtain explicit
semiclassical expansions in terms of complex trajectories that are selected
with appropriate complex-time paths. We show how this instanton-like approach,
which takes advantage of an incomplete Wick rotation, accurately reproduces
tunnelling effects not only in the usual double-well potential but also in
situations where a pure Wick rotation is insufficient, for instance dynamical
tunnelling or resonant tunnelling. Even though only one-dimensional autonomous
Hamiltonian systems are quantitatively studied, we discuss the relevance of our
method for multidimensional and/or chaotic tunnelling.
