The current study investigated the relationships predicted by the JD-R model for work engagement. Previous research has identified linear relationships between these constructs. However, there are strong theoretical arguments for testing curvilinear relationships (e.g.,Warr, 1987). Data were collected via a self-report online survey from officers of an Australian police service (N = 2,626). Results demonstrated a curvilinear relationshipbetween supervisor support and work engagement. Gender (as a control variable) was also found to be a significant predictor of work engagement. The results indicated that male police officers experienced significantly higher job demands and colleague support than female officers. However, female police officers reported significantly higher levels of work engagement than male officers. This study emphasises the need to test curvilinear relationships, as well as simple linear associations, when measuring psychological health.