The European Union (EU), Japan, and the United States (US) have recently announced initiatives to improve market access for the poorest countries. The authors assess the impact on Sub-Saharan Africa of these initiatives, and others that might be taken. They find that fully unrestricted access to all the Quad countries (Canada, The EU, Japan, and the US) would produce substantial gains for Sub-Saharan Africa, leading to a fourteen percent increase in non-oil exports (2.5 billion), and boosting real incomes by about one percent (1.8 billion). Most of these gains would come from preferential access to the highly protected Japanese, and European agricultural markets, especially the heavily protected Japanese market for meat, and certain cereal grains. The smallness of Sub-Saharan Africa's trade ensures that the costs of trade diversion for the Quad, other developing countries, and the world, would be on the whole, negligible. One concern, however, is that preferential access to protected markets might lead Sub-Saharan Africa to produce goods in which it does not have a global comparative advantage, and the future erosion of these preferences might lead to adjustment costs.