Runway excursion causing no damage followed a loss of control on landing by Piper J3 student and instructor pilots.

Narrative

Tailwheel tire had been aired up to recommended pressure prior to this flight. My student had done several 3-point landings without difficulty and she was attempting a wheel landing. She got a little bit of a swerve going on the landing; but it was not excessive. When the tailwheel was lowered to the runway; however; a very rapid shimmy occurred that caused there to be no traction on the tailwheel. I attempted to correct the problem with full application of rudder and a little power; and this stopped the swerve. We were too close to the edge of the runway at this time; however; and departed into the grass. No damage occurred to the aircraft or airport. While adding air to a tire does not usually call for a test flight; it might have been a help in this instance. Not allowing the student to get even a little bit out of shape on landing would have helped too; but with a correctly functioning tailwheel it would not have been a problem for either pilot to correct the swerve. It is very important that all equipment on the aircraft are in correct operating condition. The aircraft had been inspected on a couple of occasions for tailwheel shimmy problems and I thought it was under control.