In ultrasonic devices consisting of serially coupled tuned components, components whose tuned length dimension is large compared to other dimensions, or components with profiles designed for high gain, the response of the device during operation is often characterised by modal interactions, and especially the excitation of combination resonances. The effects on ultrasonic devices are high noise levels, component failures and poor operating performance. In this paper, energy exchanges between modes are characterised to illustrate the adverse effects of combination resonances. Design solutions are proposed to eliminate these effects which concentrate on reducing the number of modes. In particular, a novel half-wavelength three-blade cutting system tuned to the first longitudinal mode has been designed by finite element modelling. An experimental investigation demonstrates that the measured response does not show evidence of modal interactions.