How to appropriately treat the ``non-MHD'' regions around magnetic null points/lines is a long standing problem in MHD modeling of processes involving collisionless magnetic reconnection. We modify the ideal MHD approach by incorporating nongyrotropic corrections to the magnetic induction equation. The advantage of our approach is that the nongyrotropic corrections can be expressed through local profiles of macroscopic parameters (magnetic field, bulk flow velocity, density, pressure) and that any ad hoc parameters such as anomalous resistivity are not required. MHD simulations with such nongyrotropic corrections reproduce fast reconnection rates observed in and Hall-MHD simulations with similar setups. We demonstrate that ``Hall term'' is not the critical factor as soon as nongyrotropic corrections are included.