This document proposes algorithms for efficiently mining closed+ high utility itemsets (CHUIs) from transactional databases. CHUIs provide a concise lossless representation of all high utility itemsets (HUIs). The algorithms AprioriCH, AprioriHC-D, and CHUD are proposed to mine CHUIs. Additionally, the DAHU method derives all HUIs from the set of CHUIs without accessing the original database. Experimental results show the proposed algorithms achieve significant speedups and space savings compared to state-of-the-art HUI mining algorithms.