Draw the corners using boxes that overlay each other, decreasing in height, increasing in width. Tested with Konqueror, Mozilla (1.7), MS IE 6.

Testing: "Rounded corners using ONLY CSS and NO IMAGES!"
More text...

 

Here is the HTML code with embedded style info:

<div style="margin: 0 4px 0 4px; padding:0; border: solid 1px #000; background-color:#ffc000; z-index:1;">
  <div style="margin: 0 -2px 0 -2px; padding:1px; border-left: solid 1px #000;border-right: solid 1px #000; background-color:#ffc000; z-index:2;">
    <div style="margin: 0 -3px 0 -3px; padding:1px; border-left: solid 1px #000;border-right: solid 1px #000; background-color:#ffc000; z-index:3;">
      <div style="margin: 0 -3px 0 -3px; padding:1px; border-left: solid 1px #000;border-right: solid 1px #000; background-color:#ffc000; z-index:4;">
        <div style="margin: 0 -3px 0 -3px; padding: 0 4px 0 4px; border-left: solid 1px #000; border-right: solid 1px #000; background-color:#ffc000; z-index:5;">
          ------> CONTENTS OF BOX GOES HERE <------
        </div>
      </div>
    </div>
  </div>
</div>