The classical Wolter Type 1 X-ray telescope consists of two grazing incidence mirrors, a confocal paraboloid and hyperboloid. This design exhibits perfect geometric imaging on-axis (i.e., no spherical aberration) but suffers from severe field curvature, coma, astigmatism, and higher-order aberrations such as oblique spherical aberration. The Wolter-Schwarzschild design, consisting of two general aspheric grazing incidence surfaces, is corrected for both spherical aberration and coma, thus yielding very good geometrical performance at small field angles that becomes severely degraded at large field angles. The image quality criterion for stellar (small-field) X-ray telescopes is frequently expressed in terms of an on-axis fractional encircled energy, with the off-axis performance being dictated by the field-dependent aberrations characteristic of the design. A more appropriate image quality criterion for wide-angle applications is some area-weighted-average measure of resolution that maximizes the number of spatial resolution elements over a given operational field-of-view (OFOV). In practice, scattering effects from residual optical fabrication errors and detector effects (finite pixel size and charge spreading) dominate geometrical aberrations for small field angles whereas the geometrical aberrations dominate the image degradation at large field angles. Under these conditions, there is little merit in a telescope design corrected for coma (or even spherical aberration). Our new image quality criterion has led us to a whole new class of generalized Wolter Type I (hyperboloid- hyperboloid) designs that can be optimized for a given OFOV. A specific design and its predicted systems performance for the Solar X-ray Imager mission are described in detail.