One of the major shortcomings of many commonly used opioids is the fact that they are P-gp substrates, which represents a major obstacle towards effective pain management. P-gp can affect opioids’ oral absorption, CNS accumulation, systemic clearance, antinociceptive activity, and tolerance development to their analgesic effects. Moreover, P-gp can be the locus of drug–drug interactions between opioids and other concomitantly administered drugs that are P-gp substrates/inhibitors. The objective of this study was to identify opioids that are non-P-gp substrates to overcome some of the mentioned shortcomings. We evaluated the P-gp affinity status (substrate, non-substrate, or inhibitor) of a series of morphine analogs (10 opioid agonist and 2 opioid antagonists) and compared them to previously reported meperidine analogs. The fold stimulation of the morphine analogs ranged from 1.01 to 1.54 while for the meperidine analogs the fold stimulation ranged from 1.10 to 3.66. From each series (morphine and meperidine analogs) we selected potential candidate opioids that are non-P-gp substrates and conducted in vivo assessments of their antinociceptive effects using P-gp knockout and P-gp competent mice. 6-Desoxymorphine, meperidine and N-phenylbutyl normeperidine did not significantly (p > 0.05) stimulate the basal P-gp ATPase activity, where, the fold stimulations of the basal P-gp ATPase activity were 1.01 ± 0.11, 1.51 ± 0.29 and 1.10 ± 0.23, respectively. Evaluation of the influence of P-gp ablation on their antinociceptive effects indicated that P-gp did not significantly (p > 0.05) affect their antinociceptive effects. Among the evaluated opioids in vivo, 6-desoxymorphine showed high potency and induced no apparent toxicity upon low- and high-dose administration. 6-Desoxymorphine is therefore an ideal lead compound to create a library of opioids that have negligible P-gp affinity for better management of pain.