We investigate the pattern of residual speckles obtained with high-contrast coronagraphs and extreme adaptive optics systems. In particular, we provide evidence of symmetry occurring for very small phase defects depending only on the ability of the coronagraph to attenuate the pupil diffraction pattern. In such a case, a centrosymmetrical subtraction of the image significantly increases the signal-to-noise ratio. Detection of very faint companions around bright stars may benefit from this characteristic in some particular conditions. Numerical simulations show that speckle symmetry takes place when using a four-quadrant phase mask coronagraph, for very high Strehl ratio ( ) and with a filled circular aperture. SR 1 0.96