  We analyze the higher-twist effects and the SU(3)-flavour symmetry breaking
in the correlation functions used to calculate form factors of pseudoscalar
mesons in the QCD light-cone sum rule approach. It is shown that the Ward
identities for these correlation functions yield relations between twist-4 two-
and three-particle distribution amplitudes. In addition to the relations
already obtained from the QCD equations of motions, we have found a new one.
With the help of these relations, the twist-4 contribution to the light-cone
sum rule for the pion electromagnetic form factor is reduced to a very simple
form. Simultaneously, we correct a sign error in the earlier calculation. The
updated light-cone sum rule prediction for the pion form factor at intermediate
momentum transfers is compared with the recent Jefferson Lab data. Furthermore,
from the correlation functions with strange-quark currents the kaon
electromagnetic form factor and the $K\to \pi$ weak transition form factors are
predicted with $O(m_s)\sim O(m_K^2)$ accuracy.
