A human SIRPα fusion protein useful to inhibit the growth and/or proliferation of a CD47+ disease cell, the fusion protein having negligible CD47 agonism and negligible red blood cell binding, the fusion protein comprising a human SIRPα domain effective to bind human CD47 with an affinity that is at least five fold greater than the affinity of the entire extracellular region of human SIRPα, and a human IgG constant region (Fc) having effector function, the potency of the fusion protein being at least 5 fold greater than the potency of a SIRPaFc fusion formed from an Fc region lacking effector function, wherein the human SIRPα domain is an IgV domain comprising residues 32-137 [SEQ ID No.1] of human SIRPα variant 2.