The attenuation of wave modes of ultrasound propagating in a number of different diameter stainless steel wires (in the range 0.25-1.21 mm) has been found experimentally. Most modes display an attenuation minimum at certain frequencies. The varying behaviour of mode attenuation with frequency, which is called selective attenuation, is due, in part, to changing proportions of the different types of wave motion that constitute a mode. Selective attenuation is discussed in the light of two theoretical models. One model, which considers the waveguide medium as being viscoelastic in nature, is shown qualitatively to be, in reasonable agreement with experimental results but nevertheless leaves a number of questions unanswered.