Italian researchers illustrated the pain-relieving capabilities of non-psychoactive cannabinoids like CBD and CBC. However, they noted that THC was better at relieving pain. For people that get anxiety from high amounts of THC, though, CBC could be a safer alternative.
Another study from 1983 noted that the analgesic properties of THC were enhanced by adding a dose of cannabichromene to the mix.
A 2011 paper published in the British Journal of Pharmacology found CBD and CBC provided pain relief by interacting with several proteins involved with the sensory nervous system.