The growth rate of the linearised drift-tearing mode is found to be a non monotonic funtion of the stability parameter Δ′. It reaches a maximum for Δ′ ~ 0.5 Δ′1 > 0 and becomes negative for Δ′ >~ Δ′1, corresponding to the regime where the constant-approximation breaks dawn. A second mode, identified as the diamagnetic modification of the η1/3 – mode near the condition for ideal magnetohydrodynamics marginal stability, becomes unstable for Δ′ >~ Δ′2 > Δ′1 leaving a stable window of values of Δ′.