Syncing JIRA custom fields

We rely a lot on custom fields in JIRA. Is it possible for the JIRA integration app to pull custom fields? Checking the documentation, it leads me to believe this is not supported. That significantly limits the usefulness of the JIRA integration, to be honest, and forces us to explore building a custom integration with the API or SDK to accomplish it.

Has anyone solved this problem?

Thanks!
Dustin