912ULS rough at throttle back

Many owners report a vibration at the rpms you have listed. It's the nature of the beast. Harmonis and even the prop and wind can play a part. Some engines in many types of applications have a harmoic vibration at rpms that a mfg may not recommened running at. Most engines are designed to run at certain rpm's for their specific application. This is one reson we don't cruise at those rpm's all the time. Fine for coming into a patteren, but since you know where you vibation is then it's easy to avoid.

Thanks a lot Roger! It's good to know that it is not a severe problem... I was wondering why I am only finding this rough running when I reduce power and no when adding power... 

As you are commenting I am avoiding running the engine at those problematic rpms, using 4800 for cruise and below 4000 for descents.

It was running smooth for 1,400 hours at all throttle settings, then began running rough and vibrating? I don’t understand how that could be a normal characteristic of an engine in an unchanged configuration.  Why would it not do this from day one then?  Something has changed.  

Thanks a lot Jim for your answer!

I am trying to find the possible cause, that I thought was on the carbs, but after the carb overhaul I improved the issue but not removed it for this 4200-4300 range when throttle back. So I need some advice about what my next check should be....

The issue is anyhow related to carburetors, as the performance was improved after carburetor's overhaul. I have smilar type of issue with unstable RPM at around 4000 RPM settings. Carburetor overhauled was not worked. In last I replaced the carburetors and the problem got settled. If possible go with carburetor replacement or change the type of fuel for few operations. I mean from petrol to AVGAS or so.