We propose a simple parametrization for the deep-inelastic diffractive cross section. It contains the contribution of $q\bar{q}$ production to both the longitudinal and the transverse diffractive structure functions, and of the production of $q\bar{q}g$ 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.

24 pages, LaTeX, figures included using epsfig