I had the same problem with a 2001 15hp version of the engine (up-tuned version of the 9.9)--so much so that I bought the 5 year warranty from Mercury before the original factory warranty expired. The motor made 5 trips back to the dealer in Sarasota without improvement. The 6th trip--to another shop-proved the fix. It seems that there is a small adjusting screw on the carb that needs be adjusted "just so" (it's actually described in the owner's manual as pointed out by the tech at the second shop). With that adjusted properly, the engine seems to work fine. Without--Not. I would say that its a mixture control but when I suggested that, the tech said it wasn't so I don't know what it actually moderates. It's above and somewhat to the right of the carb barrel as you're facing the motor from the normal user position.
"It is not so much for its beauty that the sea makes a claim upon men's hearts, as for that subtle something, that quality of air, that emanation from the waves, that so wonderfully renews a weary spirit."