For electromagnetic cascades induced by electron-neutrinos in South Pole ice, the effective volume per detector element (phototube, radio antenna, or acoustic transducer) as a function of cascade energy is estimated, taking absorption and scattering into account. A comparison of the three techniques shows that the optical technique is most effective for energies below similar to 0.5 PeV, that the radio technique shows promise of being the most effective for higher energies, and that the acoustic method is not competitive. Due to the great transparency of ice, the event rate of AGN nu(e)-induced cascades may be as much as an order of magnitude greater in ice than in water. The ratio of Glashow resonance events to non-resonant events ranges from similar to 1/3 for the hard spectrum of Stecker and Salamon to zero for the softest spectrum of Szabo and Protheroe. The radio technique will be particularly useful in the search for Glashow events and in studies of sources with very hard energy spectra.