Joystick dead zone with flight simulators

I am not an expert gamer, but I own a joystick and I would like to use it to play FlightGear (an open source flight simulator). The joystick (which is rather low quality) has a dead zone, which apparently causes more trouble than good when piloting: ideally a dead zone should protect you from small variations when you leave the stick in the equilibrium position; however, plane flying is essentially made of continuously moving the stick close to the equilibrium position, which means that you have to cross the dead zone every time you want to compensate a little in the direction opposite to the current one. This makes my movements very erratic and uncomfortable.

How is a flight simulator rig supposed to fix this problem? Or am I supposed to be able to fly a plane even if I continuously have to cross the dead zone?