Configural Frequency Analysis (CFA) is known to be a useful tool for the exploration of contingency tables. Typical applications of CFA use tables of moderate size, that is, tables that are spanned by 3 to 5 variables, each having about 3 categories. In this article, we ask whether CFA can be meaningfully applied to 2 x 2 tables. We present analytical and simulation results that suggest that, because of the dependency of tests, first order CFA which takes the main effects into account is not a suitable candidate for 2 x 2 table analysis. Zero order CFA of 2 x 2 tables is more promising because three degrees of freedom are available instead of only one for first order CFA of 2 x 2 tables.