In practice, order acceptance and production planning are often functionally separated. As a result, order acceptance decisions are made without considering the actual workload in the production system, or by only regarding the aggregate workload. We investigate the importance of a good workload based order acceptance method in over-demanded job shop environments, and study approaches that integrate order acceptance and resource capacity loading. We present sophisticated methods that consider technological restrictions, such as precedence relations, and release and due dates of orders. We use a simulation model of a generic job shop to compare these methods with straightforward methods, which consider capacity restrictions at an aggregate level and ignore precedence relations. We compare the performance of the approaches based on criteria such as capacity utilisation. The simulation results show that the sophisticated approaches significantly outperform the straightforward approaches in case of tight due dates (little slack). In that case, improvements of up to 30% in utilisation rate can be achieved. In case of much slack, a sophisticated order acceptance method is less important.