In this contribution we present evidence that perceived numerosity of a two-dimensional arrangement of dot-like items can be strongly affected by the presence of additional, structural information. Subjects estimated and adjusted the number of items in pairs of simultaneously presented stimuli. Three experiments were conducted with displayed numerosity of dot-like items as the controlled variable and line-polygons as structural information. In all three experiments we found a significant underestimation effect whose strength depended on the positioning of the polygon edges. While in Experiment 1 the positioning of polygon edges between dots (i.e. joined dots) resulted in a strong numerosity underestimation, the simple presence of polygon structures even with no grouping function gave a less intens underestimation effect in Experiment 2. Employing an eyetracker-device in a third experiment to obtain eye-movement data, additional insight into visual attentiveness processes during numerosity comparison tasks could be gained to help to explain the observed behaviour.