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Top seed Carreno Busta needed an hour and 38 minutes to dispatch his fellow Spaniard 7-6 (7-2) 6-3 in Marbella on Wednesday.
Carreno Busta won 73 per cent of points on his first serve and saved the only two break points he faced to set up a quarter-final against Soonwoo Kwon, who beat Facundo Bagnis 6-1 6-3.
Albert Ramos-Vinolas was another home contender to progress, getting the better of Ricardas Berankis 6-3 4-6 6-3, while Norbert Gombos ousted eighth seed Federico Delbonis 5-7 7-6 (7-4) 7-6 (7-1).
There were no surprises in the Sardegna Open, where all three seeds in action moved into the last eight.
Taylor Fritz, the second seed, saw the back of Andrej Martin 6-2 7-6 (7-4) to set up a meeting with Aljaz Bedene, who beat Egor Gerasimov 6-4 7-6 (7-5).
Fifth seed Jan-Lennard Struff needed only 81 minutes to defeat qualifier Liam Broady 6-4 6-2, while Nikoloz Basilashvili rallied from a set – and five match points – down to see off Jozef Kovalik 4-6 6-4 7-5.