A method for solving the integral eigenmode equation for drift waves in cylindrical (or slab) geometry is presented. A leading‐order kinematic effect that has been noted in the past, but incorrectly ignored in recent integral‐equation calculations, is incorporated. The present method also allows electrons to be treated with a physical mass ratio (unlike earlier work that is restricted to artificially smallmi/meowing to resolution limitations). Results for the universal mode and for the ion‐temperature‐gradient driven mode are presented. The kinematic effect qualitatively changes the spectrum of the ion mode, and a new ’’second region of instability’’ fork⊥ &rgr;i≳1 is found.