This paper studies the effects on a multi-product monopolist's pricing and bundling decisions of a form of regulation in which a price-cap is imposed on only the basic level of service. Conditions are given under which the screening problem faced by the multi-product monopolist can be adequately represented in a one-dimensional screening model, and it is shown that this requires strong assumptions on preferences. In both a one-dimensional and a general multi-product screening model basic service price-caps may result in higher prices for some consumers even while lowering prices for other consumers. Socially suboptimal unbundling may be induced by such regulation in the general multi-product model.