Using constrained factor mixture models (FMM) for careless response identification is still in its infancy. Existing models have overly restrictive statistical assumptions that do not identify all types of careless respondents. The current paper presents a novel constrained FMM model with more reasonable assumptions that capture both longstring and random careless respondents. We provide a comprehensive comparison of the statistical assumptions between the proposed model and two previous constrained models. The proposed model was evaluated using both real data (N = 1,455) and statistical simulation. The results showed that the model had a superior fit, stronger convergent validity with other indicators of careless responding, more accurate parameter recovery and more accurate identification of careless respondents when compared to its predecessors. The proposed model does not require additional data collection effort, and thus researchers can routinely use it to control careless responses. We provide user-friendly syntax with detailed explanations online to facilitate its use.