Press-fitting is a very common assembly process used in many fields, especially in the watchmaking industry. It consists of introducing a shaft in a hole (also called receptor) with a certain value of tightening (or interference). However, this process is not straightforward and it is often observed that some assemblies do not manage to hold out the time and function they are meant to. In order to solve this problem, influent parameters had been searched and are now studied. The shape of the receptor has appeared as a critical one. Indeed, new machining processes have been developed this last decade and we are now able to make new designs which could cope perfectly with this application. The article will deal with the influence of the two main parameters involved in a press-fitting assembly: the maximal press-fitting force, measured axially; and the resistive torque exercised between the shaft and the receptor. The main purpose will be to find which kind of design allows the contact to become less stiff, which means less internal constraints. Thus, the tolerances, especially those of the receptor (they are less well controlled than those of the shaft) could be enlarged and this would be a great improvement for the industrial world.