Ability to link issues to stories and not just epics

Jira Agile has good support for linking issues to Epics; but it doesn't have any support for linking features, improvements, bugs, tasks to Stories. It would be great to have the ability to do this, so that the epic reports roll up from the individual issues, Stories and all.

There are many cases where a story is composed of features, bugs, etc - especially issues in other projects. I get that it's not always desirable to break a story in to smaller parts; but there are times when it is.