In case anyone was wondering, when redeeming a 20K-mile award, and using a 10K-mile Quest Card discount, one only earns Premier Qualifying Points (PQP) for the Redeemable Miles (RDM) actually used, in this case 20K - 10K = 10K RDM spent, resulting in 100 PQP earned, or maybe 101 PQP if one has a fortunate breakdown of the RDM spent over two segments.