The Desert Finch, Carduelis obsoleta (formerly Rhodopechys obsoleta), has turned out to belong to the genus Carduelis as indicated by DNA sequences, song and eyestripe pattern; it shares a common ancestor with the greenfinches (Zamora et al., 2006). See the species account for details.
References
Arnaiz-Villena, A., Moscoso, J., Ruiz-del-Valle, V., Gonzalez, J., Reguera, R., Ferri, A., Wink, M., Serrano-Vela, J. I. 2008. Mitochondrial DNA Phylogenetic Definition of a Group of ‘Arid-Zone’ Carduelini Finches. The Open Ornithology Journal, Volume 1: pp.1-7. (Free download available at http://www.bentham.org/open/tooenij/openaccess2.htm) doi: 10.2174/1874453200801010001
Cabanis, Jean (1851): [Genus RhodopechysIn: Museum Heineanum. Verzeichniss der ornithologischen Sammlung des Oberamtmann Ferdinand Heine, etc.1(20): 157 (note) [in German] PDF fulltext available at Gallica: search for "Cabanis"
Groth, J. G. 1994. A mitochondrial cytochrome b phylogeny of cardueline finches. Journal für Ornithologie, 135: 31.
Zamora, Jorge; Lowy, Ernesto; Ruiz-del-Valle, Valentin; Moscoso, Juan; Serrano-Vela, Juan Ignacio; Rivero-de-Aguilar, Juan & Arnaiz-Villena, Antonio (2006): Rhodopechys obsoleta (desert finch): a pale ancestor of greenfinches (Carduelis spp.) according to molecular phylogeny. Journal of Ornithology147(3): 448–456. doi:10.1007/s10336-005-0036-2 (HTML abstract). Erratum, Journal of Ornithology147(3): 511–512 doi:10.1007/s10336-006-0072-6