First, the basis and the characteristics of the Czjzek model for the distribution of electricfield gradient (EFG) tensor in disordered solids, some of which are still unnoticed, aredepicted. That model results from the statistical invariance by rotation of the structure ofthe considered disordered solid and from the applicability of a central limit theorem to theEFG tensor. These two conditions, which are physically realistic for a wealth of disorderedsolids, simplify tremendously the derivation of the EFG distribution but at the cost of acomplete loss of structural information about the investigated solid. Next, we describe asimple extension of it which is intended to mimic a well-defined local environment,with given values of the asymmetry parameter and of the principal componentVzz of the EFG tensor, perturbed by the disorder of more remote atoms. The effect of disorderis rendered by a Gaussian (Czjzek) noise with an adjustable weight relative toVzz. The number of free parameters is limited to three, as compared to a sole scale factor forthe Czjzek model. Its characteristics are described as a function of the given asymmetryparameter and of the strength of the noise. The aim is to lead to a practical tool which mayhelp to retrieve, as far as possible, the information about the local environment perturbedby disorder from hyperfine measurements and notably from NMR spectra of quadrupolarnuclei. 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.