A central irradiating source heats an accretion disc atmosphere and structural instabilities rapidly result in irradiation-driven warping and precession (Wijers & Pringle 1998). Warps have been found in both AGN and planetary discs but the most classic example is the eclipsing X-ray binary star Her X-1. The precessing disc in this object provides an occulting body for the central X-ray source on a quasi-period of 20 orbital cycles and a shadow over the X-ray heated face of the companion star which varies on the same timescale. Disc models recreate these observations easily, but the problem of fitting three-dimensional discs to one-dimensional X-ray and optical light curves is poorly constrained. In order to put useful constraints on the disc shape we require a more robust diagnostic than standard photometry. We have developed ``Echo tomography'' to solve this problem.