During a planned full-stop landing, the airplane bounced back into the air after the initial touchdown, and then settled to the runway a second time. Almost immediately after the second touchdown, the airplane veered sharply to the left and departed the runway surface. Before the pilot could get the airplane to come to a stop, its left wing struck a tree, resulting in the airplane spinning around and coming to a stop. The pilot said that the airplane had no mechanical or directional control anomalies, and that he should have executed a go-around when the airplane first bounced back into the air.