We present an analytic design method for the reproducible fabrication of double-chirped mirrors to achieve simultaneously a high ref lectivity and dispersion compensation over an extended bandwidth compared with those of standard quarter-wave Bragg mirrors. The mirrors are fabricated by ion beam sputtering. Use of these mirrors in a Ti:sapphire laser leads to 6.5-fs pulses directly out of the laser. The method can also be applied to the design of chirped-fiber gratings and general optical filters.