  The distortion of the regular motion in a quantum system by its coupling to
the continuum of decay channels is investigated. The regular motion is
described by means of a Poissonian ensemble. We focus on the case of only few
channels K<10. The coupling to the continuum induces two main effects, due to
which the distorted system differs from a chaotic system (described by a
Gaussian ensemble): 1. The width distribution for large coupling becomes
broader than the corresponding $\chi^2_K$ distribution in the GOE case. 2. Due
to the coupling to the continuum, correlations are induced not only between the
positions of the resonances but also between positions and widths. These
correlations remain even in the strong coupling limit. In order to explain
these results, an asymptotic expression for the width distribution is derived
for the one channel case. It relates the width of a trapped resonance state to
the distance between its two neighboring levels.
