Cartel detection is one of the most basic and most complicated tasks of competition authorities. In recent years, however, variance filters have provided a fairly simple tool for rejecting the existence of price-fixing, with the added advantage that the methodology requires only a low volume of data. In this paper we analyze two aspects of variance filters: 1- the relationship established between market structure and price rigidity, and 2- the use of different benchmarks for implementing the filters. This paper addresses these two issues by applying a variance filter to a gasoline retail market characterized by a set of unique features. Our results confirm the positive relationship between monopolies and price rigidity, and the variance filter's ability to detect non-competitive behavior when an appropriate benchmark is used. Our findings should serve to promote the implementation of this methodology among competition authorities, albeit in the awareness that a more exhaustive complementary analysis is required.