The imposition of a cap on the price of gas traded in the EU is increasingly the focus of the policy debate in Europe. In a previous Policy Brief, we outlined a possible approach to contain the price of gas in the EU, while safeguarding security of supply as much as possible. In this Policy Brief we explore two aspects related to the measures outlined in the previous one: (i) How would the gas imported as LNG by the TSOs or the Single Buyer entity be allocated to the different TSOs/Member States? (ii) How would the additional costs of importing LNG with respect to the price cap for pipeline gas in the EU be recovered? In the proposed mechanism, the gas volumes to be procured through the LNG auctions would be determined by aggregating the requests of the different TSOs. Therefore, at least as a first approximation, the allocations of the procured LNG volumes to the different TSOs could be based on their respective requests. We also explore additional aspects which would need to be considered if we move beyond this first approximation. We also propose that the additional costs of importing LNG with respect to the price cap for pipeline gas in the EU be recovered through an uplift charged on final consumption. We propose different approaches in terms of uplift levels and the base on which it is charged and we compare them with respect to two criteria: revenue adequacy and the ability to provide the correct price signals to consumers to promote efficient demand reduction.