  We study the behavior of the spectra corresponding to quantum systems
subjected to a contractive noise, i.e. the environment reduces the accessible
phase space of the system, but the total probability is conserved. We find that
the number of long lived resonances grows as a power law in $\hbar$ but
surprisingly there is no relationship between the exponent of this power law
and the fractal dimension of the corresponding classical attractor. This is in
disagreement with the predictions of the fractal Weyl law which has been
established for open systems where the probability is lost under the effect of
a projective noise.
