Over the last couple of years, international lawyers have hotly debated the correct way to apply Article 31, paragraph 3(c) of the 1969 Vienna Convention on the Law of Treaties. Discussions have focused on the meaning of ‘the parties’. Traditionally this expression has always been interpreted in the stricter sense of all parties to the interpreted treaty. Voices are now raised suggesting a broader interpretation. According to this view, the correct meaning of ‘the parties’ is the two or more parties to a specific dispute. Given that the two interpretations of Article 31, paragraph 3(c) will often be mutually exclusive, international legal literature provokes a review of the possible reasons that give us ground to adopt them. This article provides such a review. It arrives at the conclusion that only the stricter interpretation can be seriously defended as being correct. First, only the stricter interpretation agrees with the clear ordinary meaning of Article 31, paragraph 3(c). Secondly, even assuming that the ordinary meaning of the provision is ambiguous, a strong case can be made in favour of the stricter interpretation using other data of interpretation, such as the context, the object and purpose of the treaty, and the preparatory work.