One recommendation, book/ticket a Star Alliance award (using UA miles) in F or C on a Star Partner (but not UA) for routings that SQ flies. Then you can switch to SQ if/when they open up inventory, which seems to happen ~ 10 days prior to departure. I did this recently for a trip that included a FRA-SIN segment originally ticketed on LH. I just rang up UA Int'l Award Res. and inquired about availability on the SQ flight, and I was able to switch to SQ. Obviously I was prepared to fly this segment on LH.