We explore the advantages of telescopes with a non-circular, elongated pupil. We simulate images for a circular- and elongated-pupil telescopes of equal aperture area, and measure the contrast for detection of faint companions around bright stars as a function of angular separation. To sample spatial frequencies in all angles the elongated-pupil telescope is rotated around the optical axis and the images added using optimal image coaddition algorithms developed by Zackay & Ofek. This design gives better contrast at lower separation for diffraction-limited images (for perfect and imperfect optics) and for seeing-limited images, compared to a circular-pupil telescope.