We have perfomed studies of the K-L(0) --> pi (+) pi (-) gamma direct emiss
ion (DE) and inner Bremsstrahlung (IB) vertices, based on data collected by
KTeV during the 1996 Fermilab fixed target run. We find a(1)/a(2) = -0.737
+/- 0.034 GeV2 for the DE form-factor parameter in the rho -propagator par
ametrization, and report on fits of the form factor to linear and quadratic
functions as well. We concurrently measure Gamma (K-L(0) --> pi (+) pi (-)
gamma ,E-gamma*: > 20 MeV)/Gamma (K-L(0) --> pi (+) pi (-)) = (20.8 +/- 0.
3) x 10(-3), and a K-L(0) --> pi (+) pi (-) gamma DE/(DE + IB) branching ra
tio of 0.683 +/- 0.011.