By combining the Sloan Digitized Sky Survey Third Data Release quasar list with the VLA FIRST survey, we have identified five objects having both broad absorption lines in their optical spectra and FR-II radio morphologies. We identify an additional example of this class from the FIRST Bright Quasar Survey, J1408+3054. Including the original FR-II-BAL object, J1016+5209, brings the number of such objects to eight. These quasars are relatively rare; finding this small handful has required the 45,000-large quasar sample of SDSS. The FR-II-BAL quasars exhibit a significant anti-correlation between radio-loudness and the strength of the BAL features. This is easily accounted for by the evolutionary picture in which quasars emerge from cocoons of BAL-producing material which stifle the development of radio jets and lobes. There is no such simple explanation for the observed properties of FR-II-BALs in the unification-by-orientation model of quasars. The rarity of the FR-II-BAL class implies that the two phases do not coexist for very long in a single quasar, perhaps less than 10{sup 5} years, with the combined FR-II, high ionization broad absorption phase being even shorter by another factor of 10 or more.