Rotary tool: How to insert bits into collet straight? I've got a rotary tool (aka Dremel) with a collet like this one (aka quick change collet):


You insert the shaft of an accessoir like a drill or diamond bit and tighten the collet nut to hold the accessoir in place. The accessoir is supposed to be centered automatically.

I want to use it to engrave a rather delicate ornament into glass. During my first tries with this tool I noticed that the diamond bit often isn't centered in the collet and creates a very wide line with chipped edges instead of the fine lines it should produce. When I start the tool I can actually see how the tip of the bit isn't centered (it looks like a double image):


When I notice this, I have to stop the tool, loosen the collet nut and wiggle the diamond bit around in the hopes of centering it by chance, then start the tool again and see if I was successfull. 

How can I insert a bit into the collet straight on the first try?

I have bought high quality bits, so I assume they are straight. I always use the collet that is just big enough to insert the bits and always push the shaft all the way in. Since I get it right sometimes, I assume the machine itself is not to blame.
it seems that you are inserting the bit in correctly, it just seems like it's not going in straight some of the times. Besides being careful when inserting the bit, I'm not sure how else to guarantee the bit is set straight without some additional tests. If you want to make sure the bit is in correctly without damaging your ornament, after you insert the bit give it a quick test on a scrap piece of material to ensure that the bit is straight. Or, if you can see that double-image effect, before engraving into your ornament just run the Dremmel tool and examine the rotation of the bit to see if you get the double-image, at which point reset the bit.