Aspects of the subject disclosure may include, for example, a transmission device that includes a transmitter that generates a first electromagnetic wave to convey data. A coupler couples the first electromagnetic wave to a single wire transmission medium having an outer surface, to forming a second electromagnetic wave that is guided to propagate along the outer surface of the single wire transmission medium via at least one guided wave mode that includes an asymmetric or non-fundamental mode having a lower cutoff frequency. A carrier frequency of the second electromagnetic wave is selected to be within a limited range of the lower cutoff frequency, so that a majority of the electric field is concentrated within a distance from the outer surface that is less than half the largest cross sectional dimension of the single wire transmission medium, and/or to reduce propagation loss. Other embodiments are disclosed.