Additive Manufacturing (AM) shops typically produce high variety, low volume products on a to-order basis. Products are first created in parallel batches at a single AM station before being subjected to several post-processing operations. While there exists an emerging literature on AM station scheduling and order book smoothing, this literature has largely neglected downstream post-processing operations, which also affect overall performance. Workload Control provides a unique production control solution for these post-processing operations, but the specific AM shop structure has been neglected in the literature. Using simulation, this study shows that load balancing via the use of workload norms, as is typical for Workload Control, becomes ineffective since the norm must allow for the operation throughput time at the AM station and for its variability. A sequencing rule for the jobs waiting to be released that inherently creates a mix of jobs that balances the workload is therefore identified as the best-performing rule. These findings reinforce the principle that load limiting should be used at upstream stations whereas sequencing should be applied at downstream stations. Finally, although the focus is on AM shops, the findings have implications for other shops with similar structures, e.g. in the steel and semi-conductor industries.