For the classical continuous-time quickest change-point detection problem it is shown that the (randomized) Shiryaev-Roberts-Pollak procedure is nearly minimax-optimal (with minimaxity understood in the sense introduced by Pollak in his seminal 1985 Annals paper) asymptotically as the false alarm risk goes to zero. The discrete-time analogue of this result was previously obtained by Pollak in 1985 in his Annals paper.