As sleep disorders have become a major concern in public health, there is strong need for a brief and sound measure for sleep problems. The purposes of the study were to 1) evaluate factor structure and measurement invariance, 2) validate the scale based on sociodemographic data and distress, and 3) provide norm values for the general population. In a representative survey of the German population N = 2515 participants (14 to 95 years) filled in the 4-item Jenkins Sleep Scale (JSS-4), sociodemographic questions and the Brief Symptom Inventory-18 (anxiety, depression, somatic symptom load). The JSS-4 was analyzed by principal component analysis, confirmatory and multi-group confirmatory factor analyses. A multiple-indicator-multiple-cause model was tested to investigate the relationship of the JSS-4 to distress and sociodemographic variables. The one-factor structure of JSS-4 was confirmed. Given the heterogeneity of facets of sleep problems captured in the four items, internal consistency of the JSS-4 was remarkably high. The JSS-4 was strictly invariant across both sexes, and partially strictly invariant across income groups and individuals living with or without a partner. With regard to the full age range, it showed partial scalar invariance. Female sex, higher age, living without a partner, lower education, lower income and increased distress were associated with more sleep problems. Calculated normative data of sleep problems allow comparisons of JSS-4 scores stratified by sex and age.