In this article a critical evaluation is given of Eysenck's Psychoticism model. It is argued that in this model two sub-models can be distinguished, which, contrary to Eysenck's presentation, cannot be regarded as true extensions of each other. With respect to one of these models, the ‚genotypic’ P-model, the theory is criticized in that both schizophrenia and affective psychosis are determined by a common genetic predisposition which can phenotypically manifest itself in variations of P. Instead of this theory, the likelihood is put forward that a high EPQ-P score, albeit in combination with a high N and a low E score (and notwithstanding the fact that criminals or psychopaths can also obtain high P scores), is (only) related to the schizoid state, and hence, that P seems to be relevant either as a predisposing factor contributing to the development of schizophrenic psychosis, or as a factor on which biological relatives of schizophrenics obtain higher scores on average than normals do. In this respect, Eysenck's theory that the non-schizoid form of psychopathy can also be found among first-degree relatives of schizophrenics, and hence, that psychopathy and schizoidia are genetically related, is also criticized. Furthermore, it is argued that Eysenck's EPQ-P scale is not optimal for measuring those traits of the schizoid personality which are independent of N and/or E. Both arguments regarding the contents of this scale and arguments with respect to the demonstrated lack of invariance of the EPQ-P factor are adduced to support this statement. Thus, an alternative scale for measuring ‚P’ (labelled S or Insensitivity) was designed by us. The S-scale is based on literature concerning the schizoid state and reflects the results of a series of principal components analyses of (potential) S items, together with N and E items, put into execution with the intention of investigating the invariance of the S factor (and of E and N) with respect to six sample and other parameters. These investigations were carried out on a large, representative sample of the Dutch population. Additional investigations were carried out concerning the reliability and validity of the three newly formed scales. The results of these investigations turned out to be very satisfactory or, in some respects, at least promising. Finally, in this article, comments are made on the nature of the S factor, comparing this dimension with both Eysenck's P factor and the dimensions Agreeableness and Conscientiousness, as proposed, for instance, in McCrae and Costa's version of Nor-man's 5-factor model. As against P, the S or Insensitivity factor seems to be only (negatively) related to Agreeableness and not to Conscientiousness. It is also argued that this finding seems to be in accord with the supposed schizoid nature of S and the criticisms levelled at Eysenck's EPQ-P scale.