The Lynx X-ray Observatory concept, under study for the 2020 NASA Decadal Survey, will require a telescope with ∼2 m 2 of effective area and a point-spread function (PSF) with ∼0.5-arc sec half-power diameter (HPD) to meet its science goals. This requires extremely accurate thin grazing-incidence mirrors with a reflective x-ray coating. A mirror coating, such as 15-nm-thick iridium, can exhibit stress exceeding 1 GPa, significantly deforming segmented mirrors and blurring the PSF. The film stress and thickness are neither perfectly repeatable nor uniform. We use finite element analysis and ray tracing to quantify the effects of integrated stress inaccuracy, nonrepeatability, nonuniformity, and postmounting stress changes on segmented mirrors. We find that if Lynx uses segmented mirrors, it will likely require extremely small film stress (∼10 MPa) and nonuniformity (<1%). We show that realigning mirrors and matching complementary mirror pairs can reduce the HPD from uniform film stress by a factor of 2.3× and 5×, respectively. Doubling mirror thickness produces much less than the 4× HPD reduction that would be expected from a flat mirror. The x-ray astronomy community has developed numerous methods of reducing the PSF blurring from film stress, and Lynx may require several of these in combination to achieve 0.5 arc sec HPD using segmented mirrors.