For off-zenith observations with ground-based astronomical telescopes, the effect of atmospheric dispersion relative to diffraction on image size increases with telescope diameter. Correction of atmospheric dispersion in extremely large telescopes (ELTs) might become critical. A common solution for ELTs is to use linear atmospheric dispersion correctors (ADCs). In spite of their simplicity, the intrinsic chromatic aberrations of linear ADCs could render diffraction-limited imaging impossible when used in a fast focus. The chromatic problems of the linear ADC in ELTs can be resolved by replacing the linear ADC by the achromatic ADC designs presented here, which provide diffraction-limited image quality and offer several opto-mechanical advantages over linear ADCs.