Two possible ways of modifying the linear tearing mode index, by active magnetic feedback and by drift kinetic effects of deeply trapped particles, are analytically investigated. Magnetic feedback schemes, studied in this work, are found generally stabilizing for Δ′. The drift kinetic effects from both thermal particles and hot ions tend to reduce the power of the large solution from the outer region. This generally leads to a destabilization of Δ′ for the toroidal analytic equilibria considered here.