The issue of tuning the relative height of the first two dehydrogenation barriers of methane (CH(4) --> CH(3) + H and CH(3) --> CH(2) + H) is addressed using density-functional theory. It is shown that the combination of a very active reaction center-such as Rh-with a more inert substrate-such as Cu(111)-may hinder the second dehydrogenation step with respect to the first, thus resulting in the reverse of the natural order of the two barriers' heights.