We indicate that in a maximum entropy setting, the thermodynamic β and the observation constraint are linked, so that fluctuations of the latter imposes fluctuations of the former. This gives an alternate viewpoint to ‘superstatistics’. While a Gamma model for fluctuations of the β parameter gives the so-called Tsallis distributions, we work out the case of a Gamma model for fluctuations of the observable, and show that this leads to K-distributions. We draw attention to the fact that these heavy-tailed distributions have high interest in physical applications, and we discuss them in some details.