The principle of DEPENDENCY LENGTH MINIMIZATION, which seeks to keep syntactically related words close in a sentence, is thought to universally shape the structure of human languages for effective communication. However, the extent to which dependency length minimization is applied in human language systems is not yet fully understood. Preverbally, the placement of long-before-short constituents and postverbally, short-before-long constituents are known to minimize overall dependency length of a sentence. In this study, we test the hypothesis that placing only the shortest preverbal constituent next to the main-verb explains word order preferences in Hindi (a SOV language) as opposed to the global minimization of dependency length. We characterize this approach as a least-effort strategy because it is a cost-effective way to shorten all dependencies between the verb and its preverbal dependencies. As such, this approach is consistent with the bounded-rationality perspective according to which decision making is governed by "fast but frugal" heuristics rather than by a search for optimal solutions. Consistent with this idea, our results indicate that actual corpus sentences in the Hindi-Urdu Treebank corpus are better explained by the least effort strategy than by global minimization of dependency lengths. Additionally, for the task of distinguishing corpus sentences from counterfactual variants, we find that the dependency length and constituent length of the constituent closest to the main verb are much better predictors of whether a sentence appeared in the corpus than total dependency length. Overall, our findings suggest that cognitive resource constraints play a crucial role in shaping natural languages.