Process models need to reflect the real behavior of an organization's processes to be beneficial for several use cases, such as process analysis, process documentation and process improvement. One quality criterion for a process model is that they should precise and not express more behavior than what is observed in logging data. Existing precision measures for process models purely focus on the control-flow dimension of a process model, thereby ignoring other perspectives, such as the data objects manipulated by the process, the resources executing process activities, and time-related aspects (e.g., activity deadlines). Focusing on the control-flow only, the results may be misleading. This paper extends existing precision measures to incorporate the other perspectives and, through an evaluation with a real-life process and corresponding logging data, demonstrates how the new measure matches our intuitive understanding of precision.