William II of England

Context: William went hunting on 2 August 1100 in the New Forest, probably near Brockenhurst, and was killed by an arrow through the lung, though the circumstances remain unclear. The earliest statement of the event was in the Anglo-Saxon Chronicle, which noted that the king was "shot by an arrow by one of his own men." Later chroniclers added the name of the killer, a nobleman named Walter Tirel, although the description of events was later embroidered with other details that may or may not be true. The first mention of any location more exact than the New Forest comes from John Leland, who wrote in 1530 that William died at Thorougham, a placename that is no longer used, but that probably referred to a location on what is now Park Farm on the Beaulieu estates.  The king's body was abandoned by the nobles at the place where he fell. A peasant later found it. William's younger brother, Henry, hastened to Winchester to secure the royal treasury, then to London, where he was crowned within days, before either archbishop could arrive. William of Malmesbury, in his account of William's death, stated that the body was taken to Winchester Cathedral by a few countrymen.  To the chroniclers - men of the Church - such an "act of God" was a just end for a wicked king, and was regarded as a fitting demise for a ruler who came into conflict with the religious orders to which they belonged. Over the following centuries, the obvious suggestion that one of William's enemies had a hand in this event has repeatedly been made: chroniclers of the time point out themselves that Tirel was renowned as a keen bowman, and thus was unlikely to have loosed such an impetuous shot. Moreover, Bartlett says that rivalry between brothers was the pattern of political conflict in this period. William's brother Henry was among the hunting party that day and succeeded him as King.  Modern scholars have reopened the question, and some have found the assassination theory credible or compelling, but the theory is not universally accepted. Barlow says that accidents were common and there is not enough hard evidence to prove murder. Bartlett notes that hunting was dangerous. Poole says the facts "look ugly" and "seem to suggest a plot." John Gillingham points out that if Henry had planned to murder his brother it would have been in his interest to wait until a later time. It looked as though there would soon be a war between William and his elder brother Robert, which would result in one of them being eliminated, thus opening the way for Henry to acquire both England and Normandy through a single assassination. Tirel fled immediately. Henry had the most to gain by his brother's death. Indeed, Henry's actions "seem to be premeditated: wholly disregarding his dead brother, he rode straight for Winchester, seized the treasury (always the first act of a usurping king), and the next day had himself elected."  William's remains are in Winchester Cathedral, scattered among royal mortuary chests positioned on the presbytery screen, flanking the choir. His skull appears to be missing, but some long bones may remain. CANNOTANSWER

Question: Besides the information about William II of England being shot, what did the other account say?
Answer: Later chroniclers added the name of the killer, a nobleman