  We investigate how decoherence affects the short-time separation between
quantum and classical dynamics for classically chaotic systems, within the
framework of a specific model. For a wide range of parameters, the distance
between the corresponding phase-space distributions depends on a single
parameter $\chi$ that relates an effective Planck constant $\hbar_{\rm eff}$,
the Lyapunov coeffficient, and the diffusion constant. This distance peaks at a
time that depends logarithmically on $\hbar_{\rm eff}$, in agreement with
previous estimations of the separation time for Hamiltonian systems. However,
for $\chi\lesssim 1$, the separation remains small, going down with $\hbar_{\rm
eff}^2$, so the concept of separation time loses its meaning.
