Fall detection is a very important challenge that affects both elderly people and the carers. Improvements in fall detection would reduce the aid response time. This research focuses on a method for fall detection with a sensor placed on the wrist. Falls are detected using a published threshold-based solution, although a study on threshold tuning has been carried out. The feature extraction is extended in order to balance the dataset for the minority class. Alternative models have been analyzed to reduce the computational constraints so the solution can be embedded in smart-phones or smart wristbands. Several published datasets have been used in the Materials and Methods section. Although these datasets do not include data from real falls of elderly people, a complete comparison study of fall-related datasets shows statistical differences between the simulated falls and real falls from participants suffering from impairment diseases. Given the obtained results, the rule-based systems represent a promising research line as they perform similarly to neural networks, but with a reduced computational cost. Furthermore, support vector machines performed with a high specificity. However, further research to validate the proposal in real on-line scenarios is needed. Furthermore, a slight improvement should be made to reduce the number of false alarms.