Segmented X-ray telescope mirrors fabricated from thin silicon substrates are being developed by a group at the NASA Goddard Space Flight Center for future generation telescopes such as the Lynx mission concept. The Goddard team has demonstrated high precision silicon mirrors with high angular resolution (∼1'') manufactured by a simple, low cost process. However, the required high-Z optical coatings on mirror front surfaces are difficult to deposit without significant compressive thin film stress, which threatens to distort mirrors and negate the benefits of the high quality substrates. Coating stress reduction methods have been investigated by several groups, but none to date have reported success on real mirrors to the required tolerances. In this paper, we report a new method for correcting mirrors with stress-induced distortion which utilizes a micro-patterned silicon oxide layer on the mirror's back side. Due to the excellent lithographic precision of the patterning process, we demonstrate stress compensation control to a precision of ∼0.3%. The proposed process is simple and inexpensive due to the relatively large pattern features on the photomask. The correction process has been tested on flat silicon wafers with 30 nm-thick chrome coatings under compressive stress and achieved surface slope improvements of a factor of ∼80. We have also successfully compensated two iridium-coated silicon mirrors provided by the Goddard group. The RMS slope errors on coated mirrors after compensation were only degraded by ∼0.06 arc-seconds RMS axial slope compared to the initial uncoated state.