Истрад-Тиви
Gruffydd then turned his attention to the conquest of Deheubarth, ruled by his maternal cousin Hywel ab Edwin of the House of Dinefwr. The latter was "by no means easy to dislodge", wrote Lloyd. Gruffydd raided Deheubarth's province of Ceredigion in 1036, ravaging the lands of the monastic community of Llanbadarn Fawr (Great Llanbadarn). Hywel of Deheubarth was able to defend Deheubarth against Gruffydd's raids until he was defeated in 1041 at the Battle of Pencader, after which Gruffydd captured Hywel's wife and became master of Ceredigion. Following the Battle of Pencader, Hywel retained Dyfed (Pembrokeshire) and Ystrad Tywi (Carmarthenshire), the heart of Deheubarth. However he was expelled by Gruffydd in 1043 after an unrecorded event, and sought refuge in Ireland. In 1044 Hywel returned to recover Deheubarth with an army of Hiberno-Norse, but was slain and defeated in the Battle of Aber Tywi by Gruffydd ap Llywelyn.