An important puzzle in corporate taxation is that effective tax rates have fallen significantly while tax revenue has simultaneously risen in most countries. Moreover, the gross profitability of firms seems to be lower in high-tax countries, even though standard models of international investment would yield the opposite conclusion. We offer an explanation for these stylized facts by setting up a simple two-country model of tax competition with heterogeneous firms. In this model a unique, asymmetric Nash equilibrium can be shown to exist, provided that countries are sufficiently different with respect to their exogenous market conditions. In equilibrium the larger country levies the higher tax rate and attracts the high-cost firms. A simultaneous expansion of both markets intensifies tax competition and causes both countries to reduce their tax rates, despite higher corporate tax bases.