  We derive constraints on the asymmetry a1 of the momentum fractions carried
by quark and antiquark in K and K* mesons in leading twist. These constraints
follow from exact operator identities and relate a1 to SU(3) breaking
quark-antiquark-gluon matrix elements which we determine from QCD sum rules.
Comparing our results to determinations of a1 from QCD sum rules based on
correlation functions of quark currents, we find that, for a1^\parallel(K*) the
central values agree well and come with moderate errors, whereas for a1(K) and
a1^\perp(K*) the results from operator relations are consistent with those from
quark current sum rules, but come with larger uncertainties. The consistency of
results confirms that the QCD sum rule method is indeed suitable for the
calculation of a1. We conclude that the presently most accurate predictions for
a1 come from the direct determination from QCD sum rules based on correlation
functions of quark currents and are given by: a1(K) = 0.06\pm 0.03,
a1^\parallel(K*) = 0.03\pm 0.02, a1^\perp(K*) = 0.04\pm 0.03.
