Summary: A CSP search algorithm, like FC or MAC, explores a search tree during its run. Every node of the search tree can be associated with a CSP created by the refined domains of unassigned variables. If the algorithm detects that the CSP associated with a node is insoluble, the node becomes a dead-end. A strategy of pruning “by analogy” states that the current node of the search tree can be discarded if the CSP associated with it is “more constrained” than a CSP associated with some dead-end node. In this paper we present a method of pruning based on the above strategy. The information about the CSPs associated with dead-end nodes is kept in the structures called responsibility sets and kernels. We term the method that uses these structures for pruning RKP, which is abbreviation of \(\underline{\text{R}}\text{esponsibility}\) set, \(\underline{\text{K}}\text{ernel}\), \(\underline{\text{P}}\text{ropagation}\). We combine the pruning method with algorithms FC and MAC. We call the resulting solvers FC-RKP and MAC-RKP, respectively. Experimental evaluation shows that MAC-RKP outperforms MAC-CBJ on random CSPs and on random graph coloring problems. The RKP-method also has theoretical interest. We show that under certain restrictions FC-RKP simulates FC-CBJ. It follows from the fact that intelligent backtracking implicitly uses the strategy of pruning “by analogy.”