The weighing-room great, who is planning to retire at the end of the campaign, made the trip principally to partner Hard One To Please for trainer Annike Bye Hansen in the Stockholm Cup International.
Run over just short of a mile and a half, Hard One To Please won the Group Three last year, when he beat the Archie Watson-trained Outbox in a photo.
That rival was in the field once again and chased along early he took an early lead for Hollie Doyle, with Dettori settling in early before eventually letting his mount stride on to challenge Outbox.
However, Doyle was eager to cling to the initiative and Hard One To Please dropped away before the home turn, leaving Outbox to go for home.
French raider Big Call tried his best in the final furlong, but it was Espen Hill who finished best of all down the middle of the track to grab victory for rider-trainer Madeleine Smith.
For Outbox it was a third successive runner-up spot having also been beaten in 2021, while Hard One To Please trailed home in ninth.
Dettori shook off that disappointment to team up again with Hansen in the following Listed Lanwades Stud Stakes, with Takeko coming home a cosy winner over a mile.
Doyle and Outbox’s owners Hambleton Racing also enjoyed a measure of compensation for their Stockholm Cup reverse, as the Kevin Ryan-trained Washington Heights won the Listed Bro Park Sprint Championship earlier on the card.
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