The Gram-Charlier expansion of a band is an expansion in Hermite polynomials multiplied by exponentials, which converges in the mean to the correct band shape, and its coefficients are linear combinations of moments of the band. It is shown here how this expansion can be used to simulate the vibronic band shapes resulting from various types of Jahn-Teller coupling. This process has the advantage of being at its best when the coupling is strong and the standard methods are difficult.