Famous Name justified cramped odds of 2-5 when proving much the best horse in the Group Three Keeneland International Stakes at the Curragh.
Dermot Weld's four-year-old chased home Casual Conquest in the Tattersalls Gold Cup earlier in the season before running away with a Listed prize at this venue last month.
His jockey Pat Smullen always appeared to have matters in hand and he only had to be kept up to his work to beat Staying On by two lengths.
Weld said: "He won as well as we expected him to. He keeps gaining confidence every time he wins and it was a good performance. We might go for the Prix Jacques le Marois in Deauville next."
Teddy Grimthorpe, racing manager to owner Khalid Abdullah, added: "He's really come back nicely, which is very pleasing, and Dermot has done a great job with him. He handles most ground and I think we have been going slightly down the wrong alley with him thinking he would be a mile-and-a-quarter or even a mile-and-a-half horse.
"Now we're sort of rethinking and thinking he might be a miler and I think we'll consider the Prix Jacques le Marois. We have various other options, including the Juddmonte International at York and possibly the Arlington Million, but I think probably now we'll be looking at mile races."
Three Rocks returned to winning ways in the Keeneland Minstrel Stakes. Jim Bolger's colt has been without a victory in six starts since scoring at Tipperary in April, but was always travelling kindly in the hands of Kevin Manning.
The four-year-old came to challenge Mad About You for the lead inside the final two furlongs, and stayed on towards the line to beat Georgebernardshaw by a length and a quarter.
Manning said: "I've been giving away a bit of ground at the start in some of his races as he can be a little bit awkward at the gate. Today he has jumped well and did everything right - he has won very easily. He's a tough and consistent horse and he handles most ground."
Bolger added: "He's a very versatile type. Anything from seven furlongs to a mile seems to suit him and as regards ground, it doesn't seem to matter."