Arguments are sometimes made attempting to justify proprietary awards to unjust enrichment claimants by reference to the ‘priority’ such awards supposedly give in the defendant's insolvency. Those justifications are variously that unjust enrichment claimants do not take insolvency risks, that the defendant's creditors would otherwise receive an underserved windfall, and that unjust enrichment claimants occupy a position analogous to secured creditors. This paper shows that such arguments are flawed. To award unjust enrichment claimants' proprietary rights is not to give them priority in their defendant's insolvency but to withdraw the right from the estate available for distribution to all the unsecured creditors, whatever their order of priority. Moreover, insolvency ‘priority’ is not the only consequence of such an award. Finally, when seen for what they are, viz arguments for the award of property rights, the justifications do not, for a number of reasons, stand up.