In a series of recent papers, Tess, a computer program based on the concept of hidden Markov random field, has been proposed to infer the number and locations of panmictic population units from the genotypes and spatial locations of these individuals. The method seems to be of broad appeal as it is conceptually much simpler than other competing methods and it has been reported by its authors to be fast and accurate. However, this methodology is not grounded in a formal statistical inference method and seems to rely to a large extent on arbitrary choices regarding the parameters used. The present article is an investigation of the accuracy of this method and an attempt to assess whether recent results reported on the basis of this method are genuine features of the genetic process or artefacts of the method.