The aims of the present study were: (1) to assess the factor structure of the SATAQ-3 in Spanish secondary-school students by means of exploratory factor analysis (EFA), confirmatory factor analysis (CFA) and exploratory structural equation modeling (ESEM) models; and (2) to study its invariance by sex and school grade. ESEM is a technique that has been proposed for the analysis of internal structure that overcomes some of the limitations of EFA and CFA. Participants were 1559 boys and girls in grades seventh to tenth. The results support the four-factor solution of the original version, and reveal that the best fit was obtained with ESEM, excluding Item 20 and with correlated uniqueness between reverse-keyed items. Our version shows invariance by sex and grade. The differences between scores of different groups are in the expected direction, and support the validity of the questionnaire. We recommend a version excluding Item 20 and without reverse-keyed items. © 2011 Elsevier Ltd.