Some HIV-infected individuals develop broadly neutralizing antibodies (bNAbs), whereas most develop antibodies that neutralize only a narrow range of viruses (nNAbs). bNAbs, but not nNAbs, protect animals from experimental infection and are likely a key component of an effective vaccine. nNAbs and bNAbs target the same regions of the viral envelope glycoprotein (Env), but for reasons that remain unclear only nNAbs are elicited by Env immunization. We show that in contrast to germline-reverted (gl) bNAbs, glnNAbs recognized diverse recombinant Envs. Moreover, owing to binding affinity differences, nNAb B cell progenitors had an advantage in becoming activated and internalizing Env compared with bNAb B cell progenitors. We then identified an Env modification strategy that minimized the activation of nNAb B cells targeting epitopes that overlap those of bNAbs.