Specifically, the saw his size and sound defensive game, and they wanted a nasty third line center, like Joel Otto. Or maybe even more of an offensive power forward like Trevor Linden.
But Eastwood was never going to be that type of player. He had no mean streak in him. And despite his natural girth, he was not overly strong. He lacked the upper body strength that he appeared to have.
As a result Eastwood carved out a career mostly as a fourth line center who showed occasional flashes of much more.
Eastwood was very good defensively. He was alert and aware, capable of anticipating the opposition's next move. He was a deceptively quick skater, which made him a regular on the penalty kill. He was also very good on faceoffs.
Offensively he was rarely a presence. He scored 87 goals in 783 career NHL games, with his best season coming in 1999-2000 when he scored 19 times with St. Louis.
His best years came with the Blues, who accepted his contributions to a hockey team for what he was, not for what he was not. He really thrived under coach Joel Quenneville.
Eastwood also played for Toronto, Winnipeg/Phoenix, New York, Chicago and Pittsburgh
After retiring Eastwood became a regular on Ottawa Senators radio broadcasts. He would also become an assistant coach with the Ottawa 67s junior team.