Interest in magnetic-tunnel junctions has prompted a re-examination of tunneling measurements through thin insulating films. In any study of metal-insulator-metal trilayers, one tries to eliminate the possibility of pinholes (small areas over which the thickness of the insulator goes to zero so that the upper and lower metals of the trilayer make direct contact). Recently, we have presented experimental evidence that ferromagnet-insulator-normal trilayers that appear from current-voltage plots to be pinhole-free may nonetheless in some cases harbor pinholes. Here, we show how pinholes may arise in a simple but realistic model of film deposition and that purely classical conduction through pinholes may mimic one aspect of tunneling, the exponential decay in current with insulating thickness.