An alternative approach to the analysis of radial eigenmodes of finite-β-modified drift waves in a sheared magnetic field is presented. As an illustration of this approach, it is applied to the universal drift mode. For the lowest (n = 0) radial eigenmode, the previous result [1] that finite-β effects are further stabilizing is recovered. For the next (n = 1) radial eigenmode, however, it is found that finite-β effects play a de-stabilizing role. The corresponding electromagnetic eigenmode structures are also obtained.