Some governments have recently called for international accords restricting the use of preferential taxes targeted to attract mobile tax bases from abroad. Are such agreements likely to discourage tax competition or conversely cause it to spread? We study a general model of competition for multiple tax bases and establish conditions for a restriction on preferential regimes to increase or decrease tax revenues. Our results show that restrictions are most likely to be desirable when tax bases are on average highly responsive to a coordinated increase in tax rates by all governments, and when tax bases with large domestic elasticities are also more mobile internationally. Our analysis allows us to reconcile the apparently contradictory results, derived from analyzing special cases, of the previous literature.