  A continuous complex rotation of time $t\mapsto t\EXP{-i\theta}$ is shown to
smooth out the huge fluctuations that characterise chaotic tunnelling. This is
illustrated in the kicked rotor model (quantum standard map) where the period
of the map is complexified: the associated chaotic classical dynamics, if
significant for $\theta=0$, is blurred out long before the Wick rotation is
completed ($\theta=\pi/2$). The influence of resonances on tunnelling rates
weakens exponentially as $\theta$ increases from zero, all the more rapidly the
sharper the fluctuations. The long range fluctuations can therefore be
identified in a deterministic way without ambiguity. When the last ones have
been washed out, tunnelling recovers the (quasi-)integrable exponential
behaviour governed by the action of a regular instanton.
