Traditionally, Plackett-Burman (PB) designs have been used in screening experiments for identifying important main effects. The PB designs whose run sizes are not a power of two have been criticized for their complex aliasing patterns, which according to conventional wisdom gives confusing results. This paper goes beyond the traditional approach by proposing an analysis strategy that entertains interactions in addition to main effects. Based on the precepts of effect sparsity and effect heredity, the proposed procedure exploits the designs' complex aliasing patterns, thereby turning their“liability”into an advantage. Demonstration of the procedure on three real experiments shows the potential for extracting important information available in the data that has, until now, been missed. Some limitations are discussed, and extensions to overcome them are given. The proposed procedure also applies to more general mixed level designs that have become increasingly popular.