Abstract <p>Studying of a nonlinear problem for differential equations in smooth functional spaces often begins with the studying the problem in weaker integrable spaces. And then follows some bootstrap like procedure of smoothness raising. The aim of this short communication is to attract the attention of the reader to a way of a possible notable simplification for different bootstrap procedures via application of mixed interpolation between integrable and smooth spaces. As an example, we present an a priori estimate for the 3D stationary Navier–Stokes system in a smooth space.</p>