Can only move element in IK rig to a limited range of places

I have modeled a stethoscope, attached a rig via automatic weights, set up an IK control bone, and wish to place the end piece on a patient. Here is the blend file: stethoscope problem.blend (8.03 MB)

This rig “works” in the sense that I am able to move the “Control stethoscope” bone around and the end piece and cord will follow. However, there is a very limited range in which I can move the end piece. If I try to move the end piece so that it rests on top of the cube…

…it’s virtually impossible. The end piece twists and turns every which way and I can’t move it where I want it to go. I need precise positioning for the end piece.

I thought by subdividing my bones and mesh verticies that it would give me more flexibility (as it is set up in the attached blend file) but it appears to have made no difference.

Any idea what I’m doing wrong?

Never mind. I think I figured it out. I didn’t need to use as many bones as I did; I ended up using only about 10 bones. Although I put an IK control bone in approximately the same spot as in my original example (and made it control only 3 bones), I put another IK control bone three bones prior to that (which controlled the rest of the chain), so the stethoscope end piece is located between the two IK bones.

It appears that I now have much more control over where the cable goes and how to situate the stethoscope end piece. I’m not sure if that’s the best way to solve it, but I think it’s going to work. Suggestions are absolutely welcome, though!