Similarity queries searching for the most similar objects in a database compared to a given sample object are an important requirement for multimedia databases. However, strict mathematical correctness is not essential in many applications of similarity queries. For example, if we are concerned with image retrieval based on color and texture similarity, slight mathematical inaccuracies will hardly be recognized by the human observer. Therefore we present a relaxed algorithm to perform similarity queries for multidimensional index structures. This algorithm assures only that a user defined portion of the result list containing n elements actually belongs to the n most similar objects — the remaining elements are subject to a best effort semantics. As we will demonstrate, this allows to improve the performance of similarity queries by about 25 % with only marginal inaccuracies in the result.