The rigorous study of metastability requires knowledge of the behavior of systems under various constraints. Such constraints, though impossible to impose analytically for realistic systems, are easily applied in computer simulations. We study the superheated Lennard-Jones liquid in the void-constrained ensemble, in which limits are imposed on the maximum size of voids that are allowed to form. The equation of state is sensitive to the severity of the void constraint, the more so the higher the temperature and the larger the degree of superheating. In contrast, the equation of state is insensitive to bounds placed on the magnitude of allowed density fluctuations in which both voids and clusters are restricted. Constraints that truncate the void size distribution, eliminating the large-void tail, lead to artificially high tensions. Over the range of conditions investigated here, this occurs when the size of the maximum allowed void does not exceed one average interparticle separation.