Dynamic Time Warping algorithm (DTW) is an effective tool for comparing two sequences which are subject to some kind of distortion. Unlike the standard methods for comparison, it is able to deal with a different length of compared sequences or with reasonable amount of inaccuracy. For this reason, DTW has become very popular and it is widely used in many domains. One of its the biggest advantages is a possibility to specify definable amount of benevolence while evaluating similarity of two sequences. It enables to percept similarity through the eyes of domain expert, in contrast with a strict sequential comparison of opposite sequence elements. Unfortunately, such commonly used definition of benevolence cannot be applied on DTW modifications, which were created for solving specific tasks (e.g. searching the longest common subsequence). The main goal of this paper is to eliminate weaknesses of commonly used approach and to propose a new flexible mechanism for definition of benevolence applicable to modifications of original DTW.