Denic and Szymanik (2024, henceforth D&S) argued that recursive numeral systems optimize the tradeoff between lexicon size and average morphosyntactic complexity. In support of this claim, they showed that a broad range of attested numeral systems trade off these two quantities nearly as well as the best of a large set of artificial numeral systems. However, D&S’ artificial systems were in some respects not entirely comparable to natural ones. Here, we address this issue by creating a grammar framework that can represent both natural and artificial numeral systems, and we derive both natural and artificial numeral systems from this single framework, which ensures the comparability of the two sorts of systems. We test D&S’ original claim under these new conditions, and find support for it. We also explore the proposal that numeral systems might optimize the sum of lexicon size and average morphosyntactic complexity under a fixed weighting of the two terms, and the role of the prior distribution over numbers.