  We propose a modified voter model with locally conserved magnetization and
investigate its phase ordering dynamics in two dimensions in numerical
simulations. Imposing a local constraint on the dynamics has the surprising
effect of speeding up the phase ordering process. The system is shown to
exhibit a scaling regime characterized by algebraic domain growth, at odds with
the logarithmic coarsening of the standard voter model. A phenomenological
approach based on cluster diffusion and similar to Smoluchowski ripening
correctly predicts the observed scaling regime. Our analysis exposes unexpected
complexity in the phase ordering dynamics without thermodynamic potential.
