This tip might not be relevant for your particular Sidewinder, or you may have already done it, but...
The SideWinder control panel has a "Dead Zone" control window. With a name like "Dead Zone" you would mostly likely want to set it to the minimum. However, it is miss-named and isn't really a true dead zone. Setting it to minimum actually greatly increases sensitivity near the center of the joystick beyond a linear response causing overcontrol and porpoising. It is best to leave it at the default.