We studied eye and body movements in 16 healthy young adults who performed visual tasks in upright stance. Our objective was to investigate whether these movements could be functionally related to each other when performing a precise visual task requiring large ecological gaze shifts. We also questioned the influence of an additional counting task on these relations. The participants performed searching (precise), free-viewing (unprecise) and gaze-fixation (basic) either alone or in counting silently backwards in sevens. For the search task, the participants had to visually locate as many targets as possible in the images. For the free-viewing task, they had to watch images randomly. Based on a recent model, we expected to find negative correlations between eye and center of pressure and/or body (lower back, neck, head) movements only in the search tasks. The double search-counting task was expected to increase the number of negative correlations. The results confirmed both hypotheses in both search tasks, with relations mainly between eye and head movements (89% of the time). The subjective cognitive involvement (significantly higher in searching than in free-viewing and gaze-fixation) was significantly related to all (100%) and to half (50%) of these previous correlations in search-counting and searching, respectively. Complementarily, the participants rotated their segments and oscillated more in searching than free-viewing and more in both tasks than in gaze-fixation. This study confirmed that precise visual tasks may require the brain to control synergistic relations between eye and body movements instead of individual eye and body movements.