I push the stripped wire through the bullet as far as it will go (insulation inside the bullet) then solder the exposed end. Try to balance soldering quickly (so the insulation doesn't melt too far) with taking enough time to ensure the solder joint is not 'cold'.
To insert the bullet into the sleeve the first time, I use small needle-nose pliers to grip the wire just behind the bullet, so the tip of the pliers pushes against the lip of the bullet. With new sleeves, the metal bit does want to slide sometimes, so you may need to use a finger (or another pair of pliers) to stop it. However I've never had that problem with original sleeves, as the vinyl seems to shrink over time and grab the metal bit firmly.
The metal bit is a spring, so my feeling is that "too tight" is impossible, as long as you can get the bullet in initially. But I have occasionally had to spread new ones a bit, to get the bullet in. I use the small needle-nose as a spreading tool (since that's generally what I've got in my hand at the moment
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Removal is pretty much the opposite, grip the wire with needle nose pliers and pull firmly. It should not take enough force to separate the bullet from the wire. In fact, if the bullet/wire joint is done properly, the wire should break first! (Had that happen to me a few months ago, trying to pull wires through a rusty stator tube.)