Conductivity behavior of continuum percolation in restricted two-dimensional domains is simulated by considering systems of randomly distributed disks. The domain is restricted in that conducting objects are permitted to lie in only a portion of the domain. Such a restricted domain might better approximate some natural systems. Simulations of two-dimensional systems, based on three distributions of local conductances, are examined and found to demonstrate a power-law behavior with conductivity exponents smaller than those arising in regular lattice and continuum percolation.