High-energy neutrinos with energies above a few 10^16 eV can be measured efficiently with in-ice radio detectors which complement optical detectors such as IceCube at higher energies. Several pilot arrays explore the radio technology successfully in Antarctica. Because of the low flux and interaction cross-section of neutrinos it is vital to increase the sensitivity of the radio detector as much as possible. In this manuscript, different approaches to trigger on high-energy neutrinos are systematically studied and optimized. We find that the sensitivity can be improved substantially (by more than 50% between 10^17eV and 10^18eV) by simply restricting the bandwidth in the trigger to frequencies between 80 MHz and 200 MHz instead of the currently used 80 MHz to ~1 GHz bandwidth.
These findings inform the detector design of future Askaryan detectors and can be used to increase the sensitivity to high-energy neutrinos significantly without any additional costs. The findings also apply to the phased array trigger concept.