We present tongue-palate contact (EPG) and acoustic data on English sibilant assimilation, with a particular focus on the asymmetry arising from the order of the sibilants. It is generally known that /s#ʃ/ sequences may display varying degrees of regressive assimilation in fluent speech, yet for /ʃ#s/ it is widely assumed that no assimilation takes place, although the empirical content of this assumption has rarely been investigated nor a clear theoretical explanation proposed. We systematically compare the two sibilant orders in word-boundary clusters. Our data show that /s#ʃ/ sequences assimilate frequently and this assimilation is strictly regressive. The assimilated sequence may be indistinguishable from a homorganic control sequence by our measures, or it can be characterized by measurement values intermediate to those typical for /ʃ/ or /s/. /ʃ#s/ sequences may also show regressive assimilation, albeit less frequently and to a lesser degree. Assimilated /ʃ#s/ sequences are always distinguishable from /s#s/ sequences. In a few cases, we identify progressive assimilation for /ʃ#s/. We discuss how to account for the differences in degree of assimilation, and we propose that the order asymmetry may arise from the different articulatory control structures employed for the two sibilants in conjunction with phonotactic probability effects.