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.
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.