CD47+ disease cells, such as CD47+ cancer cells, are treated with an agent that blocks signalling via the SIRPα/CD47 axis. The agent is a human SIRPα fusion protein that displays negligible CD47 agonism and negligible red blood cell binding. The fusion protein comprises an IgV domain from variant 2 of human SIRPα, and an Fc having effector function. The IgV domain binds human CD47 with an affinity that is at least five fold greater than the affinity of the entire extracellular region of human SIRPα. The fusion protein is at least 5 fold more potent than a counterpart lacking effector function.