Piston–cylinder pairs are very common in industrial mechanisms. While a piston is primarily designed for axial reciprocating motion, the occurrence of secondary motions—lateral and rotational—due to the small clearance between the piston and the cylinder may lead to frictional contact, energy loss, wear and an increase in unwanted leakage. This study focuses on mitigating the secondary motion of a ringless piston. The influence of a Rayleigh step bearing and partial surface texturing with numerous micro-dimples on the dynamic stability of the secondary motion is studied. A linear model was used to obtain the trajectory of the secondary motion and Floquet theory was applied to analyze the stability and draw stability maps. The influence of various texturing and step parameters, including the dimple area density and aspect ratio for partial texturing, as well as the length and depth of treatment for both partial texturing and step profiles, on the stability of the secondary motion was examined. The normalization method is presented, enabling the expansion of the results for various operating conditions and geometries. Conclusions and guidelines regarding the optimal parameters, in terms of a wider stability range and higher decay rate, are formulated.