Turning 6mm down to 2mm x 15mm long?
That could be a tricky one; what is the tolerance on the 2mm? You may be able to get away with it by going from 6 down to 2 in one cut with a very sharp tool. Taking a finishing cut on the 2mm dia will probably result in a lot of taper due to deflection; 15mm is 7-1/2 x diameter which is a large ratio.
Do you have a CNC mill? I have done something similar to this on Delrin where I took 5/16" diameter down to 1/8" over a length of 3/4" by holding it vertical and interpolating around it. It was even possible to use a 0.015" corner radius cutter to leave a radius at the transition for fatigue proofing; totally impossible when turning.
It was also quicker than turning because I clamped several lengths in soft jaws per machine load.
EDIT:
If you have to turn and the length of the 6mm is short, to reduce deflection when turning it to 2mm in a single pass start with a larger size. Use 10mm, turn the 2mm in one pass then turn the 6mm. This way you may be able to get away with using a tool with a bit of nose radius to get away from a sharp corner at the transition.
Incidentally brass needs zero top rake.


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