Upper and lower bounds for the mixed mu problem have recently been developed, and here we examine the relationship of these bounds to each other and to mu. A number of interesting properties are developed, and the implications of these properties for the robustness analysis of linear systems and the development of practical computation schemes are discussed. In particular we find that current techniques can only guarantee easy computation for large problems when mu equals its upper bound, and computational complexity results prohibit this possibility for general problems. In this context we present some special cases where computation is easy and make some direct comparisons between mixed mu and "Kharitonov-type" analysis methods.