Tax reform proposals in the spirit of the "flat tax" model typically aim to reduce three parameters: the average tax burden, the progressivity of the tax schedule, and the complexity of the tax code. We explore the implications of changes in these three parameters for entrepreneurial activity, measured by counts of firm births. The Swiss fiscal system offers sufficient intra-national variation in tax codes to allow us to estimate such effects with considerable precision. We find that high average taxes and complicated tax codes depress firm birth rates, while tax progressivity per se promotes firm births. The latter result supports the existence of an insurance effect from progressive corporate income taxes for risk averse entrepreneurs. However, implied elasticities with respect to the level and complexity of corporate taxes are an order of magnitude larger than elasticities with respect to the progressivity of tax schedules.