There were two duplicate threads in the SharePoint - Excel Services forum.
One of the two I had earlier moved from the SharePoint - General forum. The other had been posted direct to Excel Services with identical content and a slightly revised Subject.
I wanted to delete the thread that had been posted direct to Excel Services as it had no replies except an identical one.
I couldn't. The Options drop down for that thread did not contain Delete Thread (but did contain Move Thread and Merge Thread).
The other thread (
http://forums.technet.microsoft.com/en-US/sharepointexcel/thread/7d701eca-ca29-43fa-b862-b8d2c62ba5fa) did include the Delete Thread option but wasn't the one of the two I wanted to delete.
Why did one thread not have the Delete Thread option?
Note: I "solved" this by merging the threads (to the one I could delete - the one with the URL above) and then deleting the duplicate posts. That worked.