Comment: 38 pagesThe core is a traditional and useful solution concept in economic theory. But in discrete exchange economies without transfers, when endowments are complex, the core may be empty. This motivates Balbuzanov and Kotowski (2019) to interpret endowments as exclusion rights and propose a new concept called exclusion core. Our contribution is twofold. First, we propose a rectification of the core to solve its problem under complex endowments. Second, we propose a refinement of Balbuzanov and Kotowski's exclusion core to improve its performance. Our two core concepts share a common idea of correcting the misused altruism of unaffected agents in blocking coalitions. We propose a mechanism to find allocations in the two cores.