A standard, no-recourse mortgage contract does not adjust when the value of the underlying collateral falls. Consequently, shocks that lower house prices may trigger one of the necessary conditions for default: negative equity. A common alternative contract attempts to prevent default by imposing full-recourse. This may cause individuals who believe they are likely to default to rent; however, it does not prevent those who buy from experiencing negative equity. I consider a contract that instead precludes negative equity by tying outstanding debt to an index of house prices. This is done in an incomplete markets model that is calibrated to match U.S. micro and macro data. I find that switching to the house-price indexed contract reduces the default rate from .72% to .11% and expands homeownership rates among the young and the poor, but pushes up the equilibrium minimum mortgage rate by 90 basis points. The volatility of net cashows to financial intermediaries also increases slightly under the new contract.