Runs rough on mid range RPM

Its unlikely to be mixture problem -

I would speculate;

more likely to be prop balance, engine mounting rubber, wheels rotating or airframe resonance.

Thank you, Sean.   I will check these speculations you bring up. One person at the hangar mentioned prop balance, but no one brought up the others.   A couple of people mentioned that the carb balance may be off at partial throttle.  I am a new Rotax owner and appreciate your thoughts. 

A fuel issue is not a likely cause at just that rpm.

It could be a couple of things. Do the cheap, easy and most common things that cause issues first. Do one thing at a time. I would first sync the carbs around 3300 - 3500 and see if it goes away. Plus don't forget to sync at idle too. This is one reason I never just sync at 2500 as the book states. It's just too far down into the idle circuit and not very representative of air and fuel flow. When I used to try 2500 for the high rpm sync the needles on the sync gauges would split apart again as you applied more throttle. Plus as you get up into the higher rpms the crossover balance tube isn't functioning like it does in the idle rpm range. I do not have that issue when I sync up around 3300 -3500 rpm. 

It could be the gearbox and or prop and it can even be wind direction impacting the prop especially as you unload the prop. 

I've always had the same problem but only when slowing down downwind, going from 5000 rpm to 3000 rpm.

If I need to re-accelerate for one reason or another from 2800 rpm to 3500 rpm for example, this does not happen...

I simply avoid staying at this speed of 3000 rpm

My synchro is perfect around 3000 rpm and 3500 rpm

I would like to understand the problem, the phenomenon is less strong when I reduce the throttle slowly to go down to 3000rpm-3500rpm.

Jacques

There are many owners that have a slight vibration at certain rpm's. Just don't stay there.