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In the 2-Club Cluster Vertex Deletion (resp., 2-Club Cluster Edge Deletion) problem the input is a graph G and an integer k , and the goal is to decide whether there is a set of at most k vertices (resp., edges) whose removal from G results in a graph in which the diameter of every connected component is at most 2. In this paper we give algorithms for 2-Club Cluster Vertex Deletion and 2-Club Cluster Edge Deletion whose running times are O ⁎ (3.104 k) and O ⁎ (2.562 k) , respectively. Our algorithms were obtained using automated generation of branching rules. Our results improve the previous O ⁎ (3.303 k) -time algorithm for 2-Club Cluster Vertex Deletion [Liu et al., FAW-AAIM 2012] and the O ⁎ (2.695 k) -time algorithm for 2-Club Cluster Edge Deletion [Abu-Khzam et al., TCS 2023]. [ABSTRACT FROM AUTHOR]