We propose a simple parametrization for the deep-inelastic diffractive cross section. It contains the contribution of q (q) over bar production to both the longitudinal and the transverse diffractive structure functions, and of the production of q (q) over bar g final states from transverse photons. We start from the hard region and perform a suitable extrapolation into the soft region. We test our model on the 1994 ZEUS and H1 data, and confront it with the H1 conjecture of a singular gluon distribution.