• Detailed simulations of a small-sized telescope with secondary optics for the Cherenkov Telescope Array, and for the first time, an attempt to show a comprehensive tolerance analysis of a Schwarzschild–Couder Cherenkov telescope. • The radius of the encircled point spread function ( Θ 80 ) for the ideal optical system is found to be approximately 1.3 arcmin for an on-axis observation and approximately 3.6 arcmin for an off-axis observation at the edge of the field of view. • Shadowing is found to be at a similar level (∼11%) to that seen with the current generation of conventional Davies–Cotton Cherenkov telescopes. • An extensive tolerance analysis highlights the importance of maintaining the correct separation distance between the secondary mirror and the focal plane in order to contain the Θ 80 parameter within the size of a single pixel. • A small circular area (radius < 150 mm) at the center of the secondary mirror can be used for calibration and alignment instrumentation.