Structures vibrate, and sometimes with frequencies that are not wanted. Structures are commonly required to be resonance-free within certain frequency ranges, and if they do have undesirable frequencies, these can be moved by changing the structure stiffness, or mass, or both. A mixed stiffness/flexibility formulation of the vibration problem presents alternative condensations to stiffness and flexibility eigenvalue equations for an altered structure. The flexibility form gives more compact equations, and this is developed to solve a parent problem where a structure has a single frequency in a nominated band, to be removed by adjusting the stiffness of a brace stressing the structure in a single way. Interestingly, if the original eigenvalue problem has a Sturm sequence, the frequency exclusion problem can be solved without determining any frequency or mode of the original structure.