Efficiency in drilling is measured by Mechanical Specific Energy (MSE). MSE is the measure of the amount of energy input required to remove a unit volume of rock, expressed in units of energy input divided by volume removed. It can be expressed mathematically in terms of controllable parameters; Weight on Bit, Torque, Rate of Penetration, and RPM. It is well documented that minimizing MSE by optimizing controllable factors results in maximum Rate of Penetration. Current methods for computing MSE make it possible to minimize MSE in the field only through a trial-and-error process. This work makes it possible to compute the optimum drilling parameters that result in minimum MSE. The parameters that have been traditionally used to compute MSE are interdependent. Mathematical relationships between the parameters were established, and the conventional MSE equation was rewritten in terms of a single parameter, Weight on Bit, establishing a form that can be minimized mathematically. Once the optimum Weight on Bit was determined, the interdependent relationship that Weight on Bit has with Torque and Penetration per Revolution was used to determine optimum values for those parameters for a given drilling situation. The improved method was validated through laboratory experimentation and analysis of published data. Two rock types were subjected to four treatments each, and drilled in a controlled laboratory environment. The method was applied in each case, and the optimum parameters for minimum MSE were computed. The method demonstrated an accurate means to determine optimum drilling parameters of Weight on Bit, Torque, and Penetration per Revolution. A unique application of micro-cracking is also presented, which demonstrates that rock failure ahead of the bit is related to axial force more than to rotation speed.