The evolution of neoclassical tearing modes (NTMs) is usually described by the generalized Rutherford equation for a symmetric magnetic island. Despite the success of this representation, various experiments have found the evidence of asymmetries in the island geometry. A generalization of the model suggests that a number of effects, such as a quasi-linear correction of the constant-¿ approximation, a shear flow or a temperature gradient across the island, might be responsible for the deformation of the island geometry. In addition, it is noted that the symmetry is broken in the radial direction also by a finite third order derivative in the equilibrium helical flux function. This paper addresses the role of these asymmetries in the growth and suppression ofNTMsin a slab geometry, with particular attention to the implications for the local current drive (ECCD) and resonant heating (ECRH) terms. The stabilizing contributions provided by electron cyclotron waves to NTMs are found to be largely unaffected by these perturbations. These results correct and extend some of the conclusions presented in Lazzaro and Nowak (2009 Plasma Phys. Control. Fusion 51 035005).