In this paper we investigate how formal software verification systems can be improved by utilising parallel assignment in weakest precondition computations. We begin with an introduction to modern software verification systems. Specifically, we review the method in which software abstractions are built using counterexample-guided abstraction refinement (CEGAR). The classical NP-complete parallel assignment problem is first posed, and then an additional restriction is added to create a special case in which the problem is tractable with an O(n2) algorithm. The parallel assignment problem is then discussed in the context of weakest precondition computations. In this special situation where statements can be assumed to execute truly concurrently, we show that any sequence of simple assignment statements without function calls can be transformed into an equivalent parallel assignment block. Results of compressing assignment statements into a parallel form with this algorithm are presented for a wide variety of software applications. The proposed algorithms were implemented in the ComFoRT Reasoning Framework and used to measure the improvement in the verification of real software systems. This improvement in time proved to be significant for many classes of software.