Hi Rich_Art - it looks like the problem is that your objects are not solids that define a closed volume.

If you select one and look at the object type indicator in the upper-right corner of the window you'll see it reads "Joined Srf" or "surface" instad of reading "Solid" like it would if the object was a fully closed volume.

The booleans mostly figure out which pieces to keep and which to discard by what volume they are contained within, and if your objects are not solids that is not really well defined so you may get pieces discarded that you didn't expect.

In order to see why an object is not a solid, set up the script here on a shortcut key:
http://kyticka.webzdarma.cz/3d/moi/#SelectNaked

Put that on something like the N key for select naked edges - then when you push that key the edges that are empty and not joined between 2 surfaces will get selected so you can see where they are.

For your outer piece it looks like there is a tiny opening at the inside area of the tip.

In order for the booleans to work properly you'll need to close that up so that piece is a solid.

Another alternative is to use the Trim command to cut the pieces with one another - Trim allows you to specifically pick which pieces you want to keep or discard, then you do a Join after that to glue the parts together.

Basically the booleans do the same kind of a job as Trim + Join but they automatically decide which pieces of things to throw away based on what volume they are in. So they're kind of like a shortcut batch operation mode of trimming/joining that you can use when you have solid objects that you're working with.

- Michael