To explore the possibility of efficient fast wave current drive in an ignited plasma in the ion cyclotron (IC) range of frequency in spite of competition from absorption by ions, we have added to the full-wave toroidal code TORIC a set of subroutines which evaluate absorption by these particles at IC harmonic resonances, using a realistic 'slowing-down' distribution function, and taking into account that their Larmor radius is comparable or even larger than the fast wave wavelength. The thermalized population of α-particles is not a serious competitor for power absorption as long as their number density is compatible with maintenance of ignition. By contrast, the energetic slowing down fraction, in spite of its even greater dilution, can absorb from the waves a substantial amount of power at the cyclotron resonance and its harmonics. An extensive exploration both in frequency and in toroidal wavenumbers using the parameters of one of the European versions of DEMO shows that three frequency windows exist in which damping is nevertheless predominantly on the electrons. Designing an antenna capable of shaping the launched spectrum to optimize current drive, however, will not be straightforward. Only in a narrow range when the first IC harmonic of tritium is deep inside the plasma on the high-field side of the magnetic axis, and that of deuterium and helium is still outside on the low-field side, it appears possible to achieve a satisfactory current drive efficiency with a conventional multi-strap antenna, preferentially located in the upper part of the vessel. Exploiting the other two windows at quite low and quite high frequencies is either impossible on first principles, or will demand novel ideas in antenna design.