If you really want to quite the noise down some you can do this...
On the right side of the motor is the CCT tensioner, it is a couple on inches down from the valve cover, it has two small bolts that hold it to the head and one big bolt in the middle.
Take a socket and remove the middle bolt, slowly pull out the bolt. There is going to be a bolt, washer, spring, and roll pin. Do not loose any of these items.
Now with the tensioner bolt removed take a really small phillips head screw driver and instert it into the hole in the CCT. You will need one with at least 6" of legnth on it so you can put some force on it.
Now pull your main seat and open the fuse panel and remove the fule pump fuse. This will ensure the bike will not start, it wont hurt it if it does but I personally dont like the bike running while I am doing this as you are somewhat fighting the motor to push the adjuster out.
Once you get to this point turn the bike on and with your screw driver in the CCT hole turn the bike over and at the same time push with moderate force on the screwdriver. What you are doing is pushing the ratchet mechanism out a noth or two. This will take up the slack in the chain an quite it down.
once done with this replace the fuse and then put the CCT bolt back in, make sure you ahve the bolt, washer, spring, and roll pin and then put all back together.
Now enjoy your new found quiteness for another 5k miles.
The bad thing about kawasaki design is that the little spring you had in your hand is the only thing try to put pressure on the CCT pintle and it just can not over come the motor when running so this is a easy way to manually ratchet the adjuster.