Low response rates among rich households are thought to be a serious problem in many applications using household surveys. The paper discusses the various ways the problem can be dealt with, and makes some recommendations for practice, including in developing countries. Under certain conditions, income-selective non-compliance with an initially randomized assignment can be corrected by reweighting the data. This requires that the surveys pick up at least some top incomes. If not, then income tax records can help, including in estimating distributional national accounts. However, tax data come with their own concerns including tax avoidance/evasion, weak coverage of informal sectors and illicit incomes, and concerns about construct validity, given the limitations of taxable income as a basis for inter-personal comparisons of economic welfare. An appropriately weighted survey-based distribution of an acceptable measure of economic welfare need not be less reliable for most purposes of distributional analysis than income-tax records, including in combination with surveys. The choice will depend on the question to be addressed, and country-specific circumstances. These measurement issues warrant further research across multiple settings. Classification-D63, I32, H31