Article 7 of the New York Convention indicates that the provisions within it do not deprive any of the interested parties from whichever right to be enforced by an arbitral award, in the shape and measure admitted under the legislation or treaties of the country in which that award is invoked. The author wonders about this principle of law enforcement —more favourable in the enforcement of arbitral awards— and enquires about the opportunity to revise the New York Convention while analysing the advantages that the principle has in three different frameworks: a) relating to the effect of the arbitral clause; b) in relation to the arbitral proceedings; c) finally, in what relates to the complicated and difficult issue of the enforcement of awards in countries where they were previously set aside ad quo. The author concludes by signalling how article 7 of the New York Convention allows for certain coordination between the Convention and the even more favourable evolution of international arbitration law.