  For systems of classical spins interacting with the bath via damping and
thermal noise, the approach is suggested to replace the white noise by a pulse
noise acting at regular time intervals $\Delta t$, within which the system
evolves conservatively. The method is working well in the typical case of a
small dimensionless damping constant $\lambda$ and allows a considerable
speed-up of computations by using high-order numerical integrators with a large
time step $\delta t$ (up to a fraction of the precession period), while keeping
$\delta t\ll\Delta t$ to reduce the relative contribution of noise-related
operations. In cases when precession can be discarded, $\delta t$ can be
increased up to a fraction of the relaxation time $\propto1/\lambda$ that leads
to a further speed-up. This makes equilibration speed comparable with that of
Metropolis Monte Carlo. The pulse-noise approach is tested on single-spin and
multi-spin models.
