We investigate the tunneling-percolation mechanism of DC transport nonuniversality for conducting particles of diameter Φ placed in series within the bonds of length Lof a regular lattice model. When L/Φ→∞ the resulting bond conductance distribution function has a power-law divergence as g→0, leading to nonuniversal values of the transport exponent. Instead, finite values of L/Φ prevent the onset of nonuniversality. However, depending on the model parameters, universality can be restricted to a very narrow region around the critical percolation threshold so that, for all practical purposes, DC tranposrt continues to behave as nonuniversal. We argue that experimentally such behaviour may be indistignuishable from that of a truly intrinsic nonuniversal system.