No Compromise is out of Baggy Green (Galileo), a winner over 1600m in Australia, and is her second Group 1 winner, after Tofane (Ocean Park), who won four Group 1 races in Australia. Another half-brother, Benaud (Reliable Man), has been Group 1-placed in Australia. Baggy Green is a half-sister to two Group 1 winners, Funstar (Adelaide), who took the Gr.1 Flight Stakes, and Youngstar (High Chaparral), winner of the Gr.1 Queensland Oaks.

Second dam Starspangled (Danehill) won a maiden race at Cork and is a full sister to Downtown, winner of the Gr.3 Give Thanks Stakes.

Third dam User Friendly (Slip Anchor) was a five-time Group 1 winner, taking the Gr.1 Oaks, the Gr.1 Irish Oaks, the Gr.1 Yorkshire Oaks, the Gr.1 St Leger and the Gr.1 Grand Prix de Saint-Cloud.

Baggy Green has a filly born in 2020 by Ocean Park and was covered by him again in 2021.