In securing the stage race win, he proved his talent as both a climber and time trialist, though not on the level of the Grand Tours.

Instead he signed with Cofidis, after his initial new employer, Linda McCartney Racing Team, went bankrupt before the season started.

His four years at Cofidis did not provide Cuesta with any more wins, his biggest result a 13th place in the 2001 Vuelta a España.

In 2005 he changed to Saunier Duval–Prodir, where he won stage 5 in the Volta a Catalunya, during the early part of the 2005 UCI ProTour season.

To commemorate this, the race organizers gave him jersey number one, normally worn by the winner of the previous edition.