Are there really no experimental limits on a light Higgs boson from kaon decay?

We reexamine the theoretical estimates of the decay K→πH and the experimental constraints on the existence of a light Higgs boson from this process. We find that (i) pole diagrams generated from the Higgs-boson--gluon coupling via a loop of heavy quarks do contribute to K→πH, (ii) there is an additional contribution to the K→πH amplitude coming from the effective KHW and πHW couplings, (iii) even if B, the unknown parameter in the chiral-Lagrangian description of K endash πH transitions, is nonzero and even if the real part of the K→πH amplitude is canceled accidentally, the imaginary contribution alone suffices to rule out a Higgs boson lighter than 2mπ, and (iv) whether Higgs bosons in the mass range 2mπ<mH<350 MeV are excluded by the imaginary part of the K→πH amplitude depends on the branching ratio of H→μ+μ- and the top-quark mass. Decay modes KL→π+π-H and K+→l+νH are briefly discussed