Basel II framework requires banks to conduct stress tests on their potential future minimum capital requirements and consider 'at least the effect of mild recession scenarios'. We propose a stress testing framework for minimum capital requirements in which banks' corporate credit risks are modeled with macroeconomic variables. We can thus define scenarios such as a mild recession and consider the resulting credit risk developments and consequent changes in minimum capital requirements. We also emphasize the importance of stress testing future minimum capital requirements jointly with credit losses. Our illustrative results based on Finnish data underline the importance of such joint modeling. We also find that stress tests based on scenarios envisaged by regulators are not likely to imply binding capital constraints on banks.