Paint /w cursor and curveTo

programming flash
1 

var sp:Sprite = new Sprite();

stage.addEventListener(MouseEvent.MOUSE_MOVE, drawIt);

var p:Array = new Array();

function drawIt(e:MouseEvent):void {
	p.push(new Object());
	p[p.length-1].x = mouseX;
	p[p.length-1].y = mouseY;
	
	if (p.length > 3) {
		sp.graphics.lineStyle(1);
		sp.graphics.moveTo(p[p.length-3].x, p[p.length-3].y);
		sp.graphics.curveTo(p[p.length-2].x, p[p.length-2].y, p[p.length-1].x, p[p.length-1].y);
	};
}
addChild(sp);

Is this the correct way to draw a smooth line between mouse movements? It kinda works, but sometimes I get weird artifacts.