No wobble at all that I have noticed, that changes when I use the adaptor chuck I ordered. I did some (for me) very tight fettling with it yesterday that needed good accuracy and it was fine. I had a little play using it as a mini lathe with 3mm styrene rod, this was great too. Again the story changes with the cheap adaptor chuck I have, possibly me not getting the part centred properly in the jaws. I think you will be very pleased with it.
Richie