The Galactic site 353.273+0.641 shows maser emission at both the 22-GHz transition of water and the 6.668-GHz transition of methanol. We argue that the methanol maser establishes the site as most likely a newly forming massive star, and the narrow velocity range of this emission establishes a reliable systemic velocity. The water maser shows weak emission at this systemic velocity and much stronger emission at a velocity blueshifted by 50 km s−1. It is a second excellent example (joining 291.270−0.719) of what must now be regarded as an emerging distinct class of massive young stellar objects showing dominant blueshifted water maser outflows. We also present new data for 351.243+0.671 that strengthen its claim to be yet another member. There appears to be no complementary class of water maser dominated by redshifted outflows. The mechanism that favours dominant blueshifted outflows in preference to redshifted outflows needs further exploration.