  We discuss recent experimental results from RHIC where the flat transverse
momentum dependence of a single-spin asymmetry has been found in inclusive
production of neutral pions. This dependence takes place in a wide region of
the transverse momenta up to $p_T=10$ GeV/c. We emphasize that similar
dependence has been predicted in the nonperturbative spin filtering mechanism
for the single-spin asymmetries in hadron interactions and present some
implications for this mechanism from the new experimental data.
