Levallois,
There were different combinations but you would have compartments for a pair of snap caps and the cleaning rod that you mentioned. Sometimes there were compartments for a spare set of barrels, a box for cloth patches, spare locks etc depending on what the original buyer ordered. Just check out the websites of Holland and Holland, Purdey, Fanzoj etc and you would get a clear of idea of what you may be missing.

Good hunting!