We extract the K+ --> pi (+)e(+)e(-) amplitude scale at q(2) = 0 from the r
ecent Brookhaven E865 high-statistics data. We find that the theoretical lo
ng-distance amplitude is in good agreement with the experimental q(2) = 0 s
cale. Lastly, we find that the observed q(2) shape is explained by the comb
ined effect of the pion and kaon form-factor vector-meson-dominance rho, om
ega and phi poles, and a charged pion loop coupled to a virtual photon -->
e(+)e(-) transition. (C) 2001 Elsevier Science B.V. All rights reserved.