We present new limits on ultra-high energy neutrino fluxes above 10 ^ { 17 } eV based on data collected by the Radio Ice Cherenkov Experiment ( RICE ) at the South Pole from 1999-2005 . We discuss estimation of backgrounds , calibration and data analysis algorithms ( both on-line and off-line ) , procedures used for the dedicated neutrino search , and refinements in our Monte Carlo ( MC ) simulation , including recent in situ measurements of the complex ice dielectric constant . An enlarged data set and a more detailed study of hadronic showers results in a sensitivity improvement of more than one order of magnitude compared to our previously published results . Examination of the full RICE data set yields zero acceptable neutrino candidates , resulting in 95 % confidence-level model dependent limits on the flux E _ { \nu } ^ { 2 } d \phi / dE _ { \nu } < 10 ^ { -6 } { GeV } / ( { cm ^ { 2 } s~ { } sr } ) in the energy range 10 ^ { 17 } < E _ { \nu } < 10 ^ { 20 } eV . The new RICE results rule out the most intense flux model projections at 95 % confidence level . ^ { * } Contact for additional information .