  We study the dipolar spin-ice model at fixed density of single excitations,
$\rho$, using a Monte Carlo algorithm where processes of creation and
annihilation of such excitations are banned. In the limit of $\rho$ going to
zero, this model coincides with the usual dipolar spin-ice model at low
temperatures, with the additional advantage that a negligible number of
monopoles allows for equilibration even at the lowest temperatures. Thus, the
transition to the ordered fundamental state found by Melko et al. in 2001 is
reached using simple local spin flip dynamics. As the density is increased, the
monopolar nature of the excitations becomes apparent: the system shows a rich
$\rho$ vs. $T$ phase diagram with "charge" ordering transitions analogous to
that observed for Coulomb charges in lattices. A further layer of complexity is
revealed by the existence of order both within the charges and their associated
vacuum, which can only be described in terms of spins --the true microscopic
degrees of freedom of the system.
