First, the basis and the characteristics of the Czjzek model for the distribution of electric field gradient (EFG) tensor in disordered solids, some of which are still unnoticed, are depicted. That model results from the statistical invariance by rotation of the structure of the considered disordered solid and from the applicability of a central limit theorem to the EFG tensor. These two conditions, which are physically realistic for a wealth of disordered solids, simplify tremendously the derivation of the EFG distribution but at the cost of a complete loss of structural information about the investigated solid. Next, we describe a simple extension of it which is intended to mimic a well-defined local environment, with given values of the asymmetry parameter and of the principal component Vzz of the EFG tensor, perturbed by the disorder of more remote atoms. The effect of disorder is rendered by a Gaussian (Czjzek) noise with an adjustable weight relative to Vzz. The number of free parameters is limited to three, as compared to a sole scale factor for the Czjzek model. Its characteristics are described as a function of the given asymmetry parameter and of the strength of the noise. The aim is to lead to a practical tool which may help to retrieve, as far as possible, the information about the local environment perturbed by disorder from hyperfine measurements and notably from NMR spectra of quadrupolar nuclei. As an example, that extension is applied to some static NMR spectra of 71Ga in covalent glasses. Calculated static 71Ga NMR lineshapes are shown as a function of the parameters of the extended model.