In this article we contrast the use of the s-expression with the BDD (Binary Decision Diagram) as a data structure for programmatically manipulating Common Lisp type specifiers. The s-expression is the \textit{de facto} standard surface syntax and also programmatic representation of the type specifier, but the BDD data structure offers advantages: most notably, type equivalence checks using s-expressions can be computationally intensive, whereas the type equivalence check using BDDs is a check for object identity. As an implementation and performance experiment, we define the notion of maximal disjoint type decomposition, and discuss implementations of algorithms to compute it: a brute force iteration, and as a tree reduction. The experimental implementations represent type specifiers by both aforementioned data structures, and we compare the performance observed in each approach.