All space–time coupling effects arising in an asymmetric optical compressor consisting of two non-identical pairs of diffraction gratings are described analytically. In each pair, the gratings are identical and parallel to each other, whereas the distance between the gratings, the groove density and the angle of incidence are different in different pairs. It is shown that the compressor asymmetry does not affect the far-field fluence and on-axis focal intensity. The main distinctive feature of the asymmetric compressor is spatial noise lagging behind or overtaking the main pulse in proportion to the transverse wave vector. This results in a degraded contrast but reduces beam fluence fluctuations at the compressor output. Exact expressions are obtained for the spectrum of fluence fluctuations and fluence root mean square that depends only on one parameter characterizing compressor asymmetry. The efficiency of small-scale self-focusing suppression at subsequent pulse post-compression is estimated.