As I understand it, Jira offerst Restful web services. A new plugin that I will be releasing next month (at Engage) allows Remedy to consume Restful web services, hopefully including Jira. Please check this out
and contact me offline if you would like a pre-release download link.
Thanks LJ. I will check with JIRA team on this and get back to you, if they are ready to post restful services.