In this note, we prove that for any tree \( T \), \( \gamma_{\leq2}(T) \leq \gamma_\gamma(T) \leq ir(T) \leq \gamma(T) \), where \( \gamma_{\leq2}(G) \) is the distance-2 domination number, \( ir(T) \) is the (lower) irredundance number, \( \gamma(T) \) is the domination number, and \( \gamma_\gamma(T) \), newly defined here, equals the minimum cardinality of a set of vertices that dominates a minimum dominating set of \( T \).