  We study the effect of a non-Gaussian noise on interstate switching activated
primarily by Gaussian noise. Even weak non-Gaussian noise can strongly change
the switching rate. The effect is determined by all moments of the noise
distribution. The explicit analytical results are compared with the results of
simulations for an overdamped system driven by white Gaussian noise and a
Poisson noise. Switching induced by a purely Poisson noise is also discussed.
