The Constellation-X Spectroscopy X-Ray Telescopes consists of segmented glass mirrors with an axial length of 200 mm, a width of up to 400 mm, and a thickness of 0.4 mm. To meet the requirement of < 15 arc-second half-power diameter with the small thickness and relatively large size is a tremendous challenge in opto-mechanics. How shall we limit distortion of the mirrors due to gravity in ground tests, that arises from thermal stress, and that occurs in the process of mounting, affixing and

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... mbling of these mirrors? In this paper, we will describe our current opto-mechanical approach to these problems. We will discuss, in particular, the approach and experiment where the mirrors are mounted vertically by first suspending it at two points.