By analysis of the mechanical equations, describing deformable mirrors, we show that the print-through is the natural property of a deformable mirror, which is completely defined by the geometry and mechanics of deformation. The print-through causes increased scattering in imaging applications, and can result in hot/cold spots in laser applications. Further development of adaptive optics for extreme UV applications would also require to address the print-through problem. We describe different ways to reduce, or completely eliminate the print-through in continuous faceplate and membrane deformable mirrors. In combination with simple hysteresis compensation, our approach allows for high-precision feedforward control of these deformable mirrors, directly in terms of Zernike modes. © 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).