Creating an HTMLDocument from a String of HTML (in Java)

I'm working on a method that takes a String of HTML and returns an analogous

 javax.swing.text.html.HTMLDocument

What is the most efficient way of doing this?

The way I'm currently doing this is to use a SAX parser to parse the HTML string. I keep track of when I hit open tags (for example, <i>). When I hit the corresponding close tag (for example, </i>), I apply the italics style to the characters I've hit in between.

This certainly works, but it's not fast enough. Is there a faster way of doing this?