The best thing I did was to go with an ER32 collet chuck for the lathe.

The reason being that the collets are closed from the front sp that work can be fitted through the spindle bore. I have a set of mt3 collets but are only suted to short lengths as the draw bar gets in the way.
I suppose you could always make a hollow draw bar is you are sticking below 10mm, on second thoughts that may not work as the mt3 thread is 3/8.
The Er collet has a wider range than most collet systems also using a collet will allow the work to be replaced for further machining.

Peter