Morphine is an alkaloid from the opium poppy used to treat pain. The potentially lethal side effects of morphine and related opioids-which include fatal respiratory depression-are thought to be mediated by μ-opioid-receptor (μOR) signalling through the β-arrestin pathway or by actions at other receptors. Conversely, G-protein μOR signalling is thought to confer analgesia. Here we computationally dock over 3 million molecules against the μOR structure and identify new scaffolds unrelated to known opioids. Structure-based optimization yields PZM21-a potent G_i activator with exceptional selectivity for μOR and minimal β-arrestin-2 recruitment. Unlike morphine, PZM21 is more efficacious for the affective component of analgesia versus the reflexive component and is devoid of both respiratory depression and morphine-like reinforcing activity in mice at equi-analgesic doses. PZM21 thus serves as both a probe to disentangle μOR signalling and a therapeutic lead that is devoid of many of the side effects of current opioids.