Having returned to Atlético, Rivas was definitely waived and, in January 2004, had a second Getafe spell, still contributing 17 games to a first ever top-flight promotion.[3] He continued to be ever-present from 2004 to 2006, as the side achieved two consecutive ninth-place finishes in La Liga.
Rivas spent the first of the following two seasons with Real Sociedad, appearing irregularly as the Basques were relegated.[2] He was loaned to second-division Cádiz CF for 2007–08,[4] in another ill-fated campaign.[5]
Rivas excelled in the following second-tier seasons with Real Sociedad, rarely missing a match and helping the club to return to the top flight in his second year.[6] He featured in 32 games in 2010–11 (31 starts), scoring against his former team Atlético Madrid[7] and Sevilla FC, both fixtures ending in home losses,[8] with the club eventually retaining its status.
In late June 2011, the 31-year-old Rivas signed for Hércules CF in division two, agreeing on a 2+1 contract.[9] He played regularly during his spell in the Valencian Community, and on 9 August 2013 joined SD Eibar of the same league.[10]
Rivas' younger brother, Marcos, was also a footballer and a midfielder. He played almost exclusively in amateur football, his biggest achievement being appearing in 13 games for AD Alcorcón in the Segunda División B.[14]