  We perform a non-perturbative chiral study of the masses of the lightest
pseudoscalar mesons. In the calculation of the self-energies we employ the
S-wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory
(UCHPT) that include the lightest nonet of scalar resonances. Values for the
bare masses of pions and kaons are obtained, as well as an estimate of the mass
of the \eta_8. The former are found to dominate the physical pseudoscalar
masses. We then match to the self-energies from Chiral Perturbation Theory
(CHPT) to O(p^4), and a robust relation between several O(p^4) CHPT
counterterms is obtained. We also resum higher orders from our calculated
self-energies. By taking into account values determined from previous chiral
phenomenological studies of m_s/\hat{m} and 3L_7+L^r_8, we determine a tighter
region of favoured values for the O(p^4) CHPT counterterms 2L^r_6-L^r_4 and
2L^r_8-L^r_5. This determination perfectly overlaps with the recent
determinations to O(p^6) in CHPT. We warn about a likely reduction in the value
of m_s/\hat{m} by higher loop diagrams and that this is not systematically
accounted for by present lattice extrapolations. We also provide a favoured
interval of values for m_s/\hat{m} and 3L_7+L^r_8.
