Now that is a question that will get you 20 different answers as most of it comes down to personal feel . For one , if you do mostly straight line upright driving your K81 will be good until you get down to the cord. My personal experience with the K81 was averaging 6000 miles before the tire needed to be replace due to tread wear .. Long before that the tire had squared off and leaves an uncomfortable feeling when you are leaned over pushing through the twisties.
Look at the wear bars on the tire. When they are done or even with the tread pattern.... Replace.
2000 km out of your tyre something not right there, when running K81s back in the days I was getting 6000 miles out of the rear tyre and well over 15000 from the front I couldn't change the front to rear as I ran a 350/19 up front but changing to Avons I am getting a lot more mileage out of the rear and they not squaring out like the K81s did or wanting to chase grooves in the road, but modern tyres these days run a bit more pressure than days gone by.
I always change front and rear at the same time and the fronts never really need to be changed at the time.
My experience with Avon RRs on my modern Bonneville was similar. On wet, I would occasionally feel rear squirming while in a slower speed turn, especially if going over a manhole cover or painted strip of pavement. Similar feel sometimes on loose sand or gravel or even "tar snakes" that suddenly appear mid corner on some of our twisty roads. Never had that squirm on same bike with Shinko 705s, which are a light duty off road tread pattern. With the k70 and k81 on Commando, never felt any tire slip in nearly 18k miles and five yrs ownership. For my style of riding, I'm quite happy with them.On bikes originally equipped with K70, K81, or TT100, I always used them - that's until I bought a bike with Avon RR. For today's riding, the Avon's are much better. I probably would not have survived college with tires like them! Riding in the snow or on dirt/gravel roads is not something I would like to try on Avons! No longer crazy enough to ride a bike in the snow and don't even know where to find a dirt road these days. I can't really remember how long Dunlop tires lasted and was too poor to change them when I should. The Avons get changed when the grooves towards the sides get reduced in depth as I tend to lean harder than most into corners and am heavier that most (not riding faster, just tighter turns). I seem to get about 3500-4000 but could probably push to 4500. If I was still college poor, probably 5000
