Deep learning based methods for single-image superresolution (SR) have drawn a lot of attention lately. In particular, various papers have shown that the learning stage can be performed on a single image, resulting in the so-called internal approaches. The SinGAN method is one of these contributions, where the distribution of image patches is learnt on the image at hand and propagated at finer scales. Now, there are situations where some statistical a priori can be assumed for the final image. In particular, many natural phenomena yield images having power law Fourier spectrum, such as clouds and other texture images. In this work, we show how such a priori information can be integrated into an internal super-resolution approach, by constraining the learned up-sampling procedure of SinGAN. We consider various types of constraints, related to the Fourier power spectrum, the color histograms and the consistency of the upsampling scheme. We demonstrate on various experiments that these constraints are indeed satisfied, but also that some perceptual quality measures can be improved by the proposed approach.