  A particular case of the fundamental Sz.-Nagy--Foias functional model for a
contraction states that a pure contraction always dilates to a pure isometry.
We are interested in the similar question for pairs, more precisely: does a
pair of commuting pure contractions always dilate to a pair of commuting pure
isometries? The purpose of this article is to identify pairs of commuting pure
contractions for which the above question has an affirmative answer. Our method
is based on an explicit structure of isometric dilation for pure pairs of
commuting contractions obtained in a recent work by Das, Sarkar and the author.
