One of the important tasks in the design of gears and gearboxes based on them is to increase the load capacity, durability and noise reduction with moderate requirements for manufacturing precision by providing elastic compliance of the teeth with simple satellite manufacturing technology. In the paper is firstly presented a base satellite in a precessional transmission. The design is rigid and non-Technological. There was simulated the workload and the results are presented as a linear deformation. Simulation was based on the special module for the calculation and analysis of complex structures using the integrated module Stress Analysis (program Autodesk Inventor Professional 2012). It uses the finite element method calculation, based on the ANSYS program. Then is shown an optimized satellite structure. This option provides an increased durability and noise reduction due to local and general tooth compliance. The main drawback of this satellite is the high laboriousness of making cut-outs in the satellite. In this satellite, by increasing the diameter of the radial channel, it is possible to reduce the wall thickness and thereby increase the compliance. The simulation results of a new satellite design are presented. Compliance increased roughly by 4 times compared to the base version. When the gear is in mesh with the satellite, due to the increased elastic compliance of the teeth, a multi-pairing mesh is achieved, which reduces the contact loads and noise, increases the service life of the transmission.