Results of single-particle tunneling experiments performed on films of indium oxide are presented. The zero-bias anomalies change character with decreasing thickness from a three-dimensional behavior to a logarithmic energy dependence. Theoretical consideration suggest a crossover from a lnV to a V12 correction to the density of states at a thickness-dependent energy. In the V12 range, where the sample exhibits a three-dimensional density-of-states anomaly, its transport properties may still be two dimensional. These expectations are experimentally confirmed. © 1982 The American Physical Society.