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