We present detailed chemical abundances of three new bright (V~11), extremely metal-poor ([Fe/H]~-3.0), r-process-enhanced halo red giants based on high-resolution, high-S/N Magellan/MIKE spectra. We measured abundances for 20-25 neutron-capture elements in each of our stars. J1432-4125 is among the most r-process-rich r-II stars, with [Eu/Fe]=+1.44+/-0.11. J2005-3057 is an r-I star with [Eu/Fe]=+0.94+/-0.07. J0858-0809 has [Eu/Fe]=+0.23+/-0.05 and exhibits a carbon abundance corrected for an evolutionary status of [C/Fe]_corr_=+0.76, thus adding to the small number of known carbon-enhanced r-process stars. All three stars show remarkable agreement with the scaled solar r-process pattern for elements above Ba, consistent with enrichment of the birth gas cloud by a neutron star merger. The abundances for Sr, Y, and Zr, however, deviate from the scaled solar pattern. This indicates that more than one distinct r-process site might be responsible for the observed neutron-capture element abundance pattern. Thorium was detected in J1432-4125 and J2005-3057. Age estimates for J1432-4125 and J2005-3057 were adopted from one of two sets of initial production ratios each by assuming the stars are old. This yielded individual ages of 12+/-6Gyr and 10+/-6Gyr, respectively.