We investigate the subset of concurrent constraint programs (ccp) which are confluent in the sense that different process schedulings lead to the same possible outcomes. Confluence is an important and desirable property as it allows the program to be understood by considering any desired scheduling rule, rather than having to consider all possible schedulings. The subset of confluent programs is less expressive than tull cop. For example it cannot express fair merge although it can express demonic merge. We give a simple closure based denotational semantics for confluent ccp. We also study admissible programs which is a subset of confluent ccp closed under composition. We consider then applications of our results to give a framework for the efficient yet accurate analysis of full ccp. The basic idea is to approximate an arbitrary ccp program by an admissible program which is then analyzed.