The Gemini Telescopes Project is a collaboration to develop two leading edge 8 metre telescopes; Gemini North on Mauna Kea, Hawaii, and Gemini South at Cerro Pachon, Chile. These telescopes will exploit the excellent natural seeing conditions of the sites for observations in the visible and near infrared To capitalise on the excellent natural image quality that these telescopes will provide, a natural guide star (NGS) adaptive optics (AO) system is being developed for Gemini North. The Gemini Adaptive Optics System (GAOS), Altair, will be a medium order, Shack-Hartmann (SH) wave-front sensor (WFS) based system running at a control loop speed of at least one kHz. Based on studies of the turbulent layers at Mauna Kea(1) the deformable mirror (DM) has been set conjugate to a fixed altitude of 6.5 kilometres to increase the isoplanatic patch diameter. The system design choices of a high speed, medium order correction, the instrument location and altitude conjugation have placed challenging demands on the reconstructor for this instrument. We present a here a few of the constraints, demands and design choices for the reconstructor. The paper will conclude with a brief summary of the project status.