Microhardness testing can be a very useful tool for studying modern materials, but is plagued by well-known experimental difficulties. Reasons for the unusual behavior of hardness data at very low loads are explored by Monte Carlo simulation. These simulations bear remarkable resemblance to the results of actual hardness experiments. The limit of hardness as load or indentation depth tends to zero is shown to depend on experimental error rather than upon intrinsic material properties. The large scatter of hardness data at very low loads is insured by the accepted definition of hardness. A new definition of hardness is suggested which eliminates much of this scatter and possesses a limit as indentation depth approaches zero. Some simple calculations are used to show the utility of this new approach to hardness testing.