Joining additional objects breaks armature I'm very new to Blender and am working with a simple collection of cylinders and a three-bone armature.

Suppose I go into Pose Mode to check rotation and find that a cylinder's accidentally been left behind in a Join. I'd like to simply Join the unattached piece but when I do it appears to break the parent connection with the bone. I anticipate making additions as my object requires more detail and am sure I'm not alone in this so I wonder what's the correct way to do this.
I had several problems. 

There were multiple stray &amp; empty Containers, which I examined and deleted.

The object hierarchy was incorrectly nested.

I may have been selecting objects to join in the incorrect order.

While none of the other Stack Exchange-suggested questions were exact duplicates they did help me to think about this correctly and solve my problem.