A DNA molecule under negative superhelical stress becomes susceptible to transitions to alternate structures. The accessible alternate conformations depend on base sequence and compete for occupancy. We have developed a method to calculate equilibrium distributions among the states available to such systems, as well as their average thermodynamic properties. Here we extend this approach to include superhelical cruciform extrusion at both perfect and imperfect inverted repeat (IR) sequences. We find that short IRs do not extrude cruciforms, even in the absence of competition. But as the length of an IR increases, its extrusion can come to dominate both strand separation and B-Z transitions. Although many IRs are present in human genomic DNA, we find that extrusion-susceptible ones occur infrequently. Moreover, their avoidance of transcription start sites in eukaryotes suggests that cruciform formation is rarely involved in mechanisms of gene regulation. We examine a set of clinically important chromosomal translocation breakpoints that occur at long IRs, whose rearrangement has been proposed to be driven by cruciform extrusion. Our results show that the susceptibilities of these IRs to cruciform formation correspond closely with their observed translocation frequencies.