Most intracranial saccular aneurysms remain asymptomatic until rupture. Yet, some unruptured lesions present with various symptoms, often related to the compression of a nerve or other intracranial tissue. An obvious question, therefore, is whether or not symptomatic unruptured lesions necessarily have a greater rupture-potential than asymptomatic ones. In this paper, we show numerically that contact constraints can have a protective effect on certain lesions. Specifically, finite element analyses of stress fields in model axisymmetric lesions, with and without the presence of a rigid contacting obstacle at the fundus, reveal that with the exception of near point loads, the constraint decreases the stresses near the fundus. Given that it is well accepted that rupture occurs when wall stress exceeds wall strength, these findings suggest that the rupture-potential will be lower in at least one sub-class of constrained versus comparable unconstrained lesions. Because of the myriad of sizes, shapes, and compositions of saccular aneurysms, however, there is a need to examine this important issue further, hopefully based on an increased awareness for clinical data on lesion-tissue interactions.