Adding formatted text to a textfield?

I want to add text to a textfield, and specify the font of that text.

.defaultTextFormat is ALMOST what I want, but not quite. To demonstrate, try this out:

var output:TextField = new TextField();

output.height=200;
output.width=500;

addChild(output);

var outputFormat:TextFormat = new TextFormat();
for (var i:int=0;i<20;i++) {
    if (Math.random()<0.3)
        output.appendText("

");
    outputFormat.size=Math.round(Math.random()*30);
    output.defaultTextFormat=outputFormat;
    output.appendText(i+'line ');
}

If you run this, you’ll find that the the font size only changes between lines. Each line is a single size, when I want to be able to have multiple sizes on the same line.

I am also open to using a textArea instead of a textField, if that will work better.