Given two finite sequences, we wish to find the longest common subsequences satisfying certain deletion/insertion constraints. Consider two successive terms in the desired subsequence. The distance between their positions must be the same in the two original sequences for all but a limited number of such pairs of successive terms. Needleman and Wunsch gave an algorithm for finding longest common subsequences without constraints. This is improved from the viewpoint of computational economy. An economical algorithm is then elaborated for finding subsequences satisfying deletion/insertion constraints. This result is useful in the study of genetic homology based on nucleotide or amino-acid sequences.