A method of designing bevel gears is given, allowing to reduce the specific sliding ratio. Specific pressure coefficients are used as an additional evaluation criterion. The mathematical relationship between the criteria used is given. A distinguishing feature of the proposed methodology is the possibility of calculating the gears using an arbitrary coefficient of profile shift for each of the gears. In doing so, the value of the radial gap equal to 0.25 of the module is retained in the gears. The Bevel Gears x64 program is used for calculations. This program was written as part of the ongoing research. As an example, it is shown that a gear with number of pinion teeth z(1) = 16 and number of wheel teeth z(2) = 20, with the coefficient of profile shift for pinion x(1) = 0.7 and for wheel x(2) = 0.7, has relatively low and fairly close values of specific sliding ratio vertical bar lambda(1max)vertical bar = 1.213 and vertical bar lambda(2max)vertical bar = 1.214 as well as specific pressure ratio theta(1) = 0.45 and theta(2) = 0.347. In similar gears (z(1) = 16, z(2) = 20), designed according to the standard methodology (x(1) = 0.17 and x(2) = -0.17), the values of the studied indicators were vertical bar lambda(1max)vertical bar = 3.165, vertical bar lambda(2max)vertical bar = 2.512, theta(1) = 0.942, and theta(2) = 0.572. Reducing specific sliding ratios vertical bar lambda(1max)vertical bar from 3.165 to 1.213 and vertical bar lambda(2max)vertical bar from 2.512 to 1.214 will reduce the slippage of tooth dedendum on the pinion and wheel in proportion (2.6 and 2.1 times, respectively). The results show a significant increase of wearresistance of the designed gears.