Actually you got that backwards Odin Doomhammer.
The County of Edessa was the shortest lasting Crusader State of them all. It was the first created, in 1098, and the first to fall, in 1146. It also didn't have any good relations with any of the greater powers in the Levant, Christian or Muslim. The only good relations that Edessa actually had was with the native Armenian population. Out of the four reigning counts, three married Armenians with the fourth and last, Joscelin II, marrying a French lady.
Imad ad-Din Zengi actually first conquered Edessa in 1144, driving Joscelin II westwards to the fortress at Turbessel. This event sparked the Second Crusade. However the Crusaders returned in 1146 following Zengi's death and recaptured the city. But Nur ad-Din recaptured the city later that same year and drove Joscelin back to Turbessel. He finally captured the count in 1150 and his wife subsquently sold Turbessel to the Roman Emperor, Megas Manouel I Komnenos. The fortress itself was conquered in 1151, making the purchase moot.