  Within the traditional frame of reduced MHD, a new rigorous perturbation
expansion provides the equation ruling the nonlinear growth and saturation of
the tearing mode for any current gradient. The small parameter is the magnetic
island width w. For the first time, the final equation displays at once terms
of order w ln(1/w) and w which have the same magnitude for practical purposes;
two new O(w) terms involve the current gradient. The technique is applicable to
the case of an external forcing. The solution for a static forcing is computed
explicitly and it exhibits three physical regimes.
