Tomislav was succeeded by Trpimir II (928–935), and Krešimir I (935–945), this period, on the whole, however, is obscure. Miroslav (945–949) was killed by his ban Pribina during an internal power struggle, losing part of islands and coastal cities. Krešimir II (949–969) kept particularly good relations with the Dalmatian cities, while his son Stjepan Držislav (969–997) established better relations with the Byzantine Empire and received a formal authority over Dalmatian cities. His three sons, Svetoslav (997–1000), Krešimir III (1000–1030) and Gojslav (1000–1020), opened a violent contest for the throne, weakening the state and further losing control. Krešimir III and his brother Gojslav co-ruled from 1000 until 1020, and attempted to restore control over lost Dalmatian cities now under Venetian control. Krešimir was succeeded by his son Stjepan I (1030–1058), who tried to reinforce the alliance with the Byzantines when he sent a segment of his naval fleet in war against the Arabs in 1032, in favour for their tolerance about conquering Zadar another Byzantine ally, from Venice. He did conquer it, but the circumstances changed later and lost it.