We study how various zoning regulations combine to affect housing supply, prices, and rents of single- and multifamily homes using novel lot-level zoning data from Greater Boston and a cross-sectional boundary discontinuity design at regulation boundaries. Looser density restrictions, alone or with other less restrictive regulations, are most effective in increasing supply and reducing per-housing-unit rents and prices. We theoretically and empirically show that restrictive zoning regulations shift housing stock towards larger units, increasing prices per housing unit. Counterfactuals imply that a recent Massachusetts law increasing building density near transit can reduce long-run rents and prices, particularly in suburbs.