Boolean Union troubles

 From:  Jacob
Hello all,

Can anyone tell me what's wrong with these four objects selected on the attached image?

You can see same four objects positioned inside the pen well, to be used as grips.

Whenever I try using boolean union (and difference) most of my "base" object is deleted, leaving only a bit of one of those objects.

They were constructed by a network using several copies of two curves - at first I tried to build them using a sweep, but it was giving me extremely wild results.

Scaling up didn't help.

Any pointers? I don't mind reworking them, just I like their shape.