  We study a spontaneous collapse model for a two-level (spin) system, in which
the Hamiltonian and the stochastic terms do not commute. The numerical solution
of the equations of motions allows to give precise estimates on the regime at
which the collapse of the state vector occurs, the reduction and delocalization
times, and the reduction probabilities; it also allows to quantify the effect
that an Hamiltonian which does not commute with the reducing terms has on the
collapse mechanism. We also give a clear picture of the transition from the
"microscopic" regime (when the noise terms are weak and the Hamiltonian
prevents the state vector to collapse) to the "macroscopic" regime (when the
noise terms are dominant and the collapse becomes effective for very long
times). Finally, we clarify the distinction between decoherence and collapse.
