"In the year 1073 a battle was fought at Llanddewi Brefi, between Gronw and Llewellyn, the sons of Cadwgan-ap-Bleddyn, and Rhys-ap-Owen and Rhyddarch-ap-Caradog, in which the princes of Powys were victorious, and Rhyddarch was slain."
Source: Tallis, Topographical Dictionary of England and Wales, 1860, p.1058.
However, The Chronicle of the Princes makes no mention of a battle in 1073, but does provide a description of a battle in 1075 [nprn 404612; 'in the Camddwr', a river which forms the eastern boundary of the community of Llanddewi Brefi (there is another river of the same name in Radnorshire)] with exactly the same combatants, but a different outcome:
1075: And then was the battle in the Camddwr between Goronwy and Llywelyn, sons of Cadwgan, and Caradog ap Gruffydd along with them, and Rhys ab Owain and Rhydderch ap Caradog. And Goronwy and Llywelyn were defeated, and Caradog along with them.
Source: Thomas Jones, The Chronicle of the Princes, 1955, p.29.
B.A.Malaws, RCAHMW, 18 July 2006.