Dependency length minimization is a universally observed quantitative property of natural languages. However, the extent of dependency length minimization, and the cognitive mechanisms through which the language processor achieves this minimization remain unclear. This research offers mechanistic insights by postulating that moving a short preverbal constituent next to the main verb explains preverbal constituent ordering decisions better than global minimization of dependency length in SOV languages. This approach constitutes a least-effort strategy because it's just one operation but simultaneously reduces the length of all preverbal dependencies linked to the main verb. We corroborate this strategy using large-scale corpus evidence across all seven SOV languages that are prominently represented in the Universal Dependency Treebank. These findings align with the concept of bounded rationality, where decision-making is influenced by 'quick-yet-economical' heuristics rather than exhaustive searches for optimal solutions. Overall, this work sheds light on the role of bounded rationality in linguistic decision-making and language evolution.