Hypervolatile species such as carbon monoxide (CO) and molecular nitrogen (N2) have been detected in comets, and could be used to constrain comet formation temperature conditions if their presence is due to freeze-out and/or entrapment. Here, we instead explore another plausible origin of cometary hypervolatiles: photodissociation of less volatile species. We characterize CO and N2 formation following ultraviolet (UV) irradiation and electron bombardment of carbon dioxide (CO2), ammonia (NH3), H2O:CO2, H2O:NH3, and H2O:CO2:NH3 cometary ice analogs. We find that CO and N2 form in all photoprocessed ices at temperatures between 10 and 100 K, resulting in 0.4%–0.9% CO and 0.03%–0.7% N2 relative to water, and CO/CO2 and N2/NH3 mixing ratios of 2.5%–62% and 0.7%–9%, respectively, across the experiments. Because our initial ices are reasonably well matched to interstellar ices and we use a UV exposure similar to a dark cloud, we can compare the resulting ratios directly to cometary abundances. Such a comparison shows that, while only a few CO observations in comets are readily explained by photodissociation, almost all observed cometary N2 can be accounted for by photodissociation of NH3 embedded in water ice. The latter result is also consistent with observed similarly elevated isotopic ratios of N2 and NH3 in 67P. Taken together, our results suggest that N2/H2O ratios <1% should be used cautiously when inferring a comet’s formation location, while the more substantial CO abundances seen in many comets do likely imply entrapment at low ice temperatures.