Previous works usually report greater postural stability in precise visual tasks (e.g., gaze-shift tasks) than in stationary-gaze tasks. However, existing cognitive models do not fully support these results as they assume that performing an attention-demanding task while standing would alter postural stability because of the competition of attention between the tasks. Contrary to these cognitive models, attentional resources may increase to create a synergy between visual and postural brain processes to perform precise oculomotor behaviors. To test this hypothesis, we investigated a difficult searching task and a control free-viewing task. The precise visual task required the 16 young participants to find a target in densely furnished images. The free-viewing task consisted of looking at similar images without searching anything. As expected, the participants exhibited significantly lower body displacements (linear, angular) and a significantly higher cognitive workload in the precise visual task than in the free-viewing task. Most important, our exploration showed functional synergies between visual and postural processes in the searching task, that is, significant negative relationships showing lower head and neck displacements to reach more expended zones of fixation. These functional synergies seemed to involve a greater attentional demand because they were not significant anymore when the cognitive workload was controlled (partial correlations). In the free-viewing task, only significant positive relationships were found and they did not involve any change in cognitive workload. An alternative cognitive model and its potential subtended neuroscientific circuit are proposed to explain the supposedly cognitively grounded functional nature of vision-posture synergies in precise visual tasks.