  A semi-lattice is said to be tree-like when any two of its elements are
either orthogonal or comparable. Given an inverse semigroup S whose idempotent
semi-lattice is tree-like, and such that all tight filters are ultra-filters,
we present a necessary and sufficient condition for S to be contracting which
looks closer in spirit to the notion of contracting actions than a recent
condition found by the second named author and E. Pardo.
