How do I avoid a page break immediately after a heading

I have an HTML 4.01/CSS 2.1 document that includes an H3 heading followed by a short (one line) paragraph block and then an unordered list with several items:

<h3>Heading!</h3>

<p>Some things:</p>

<ul>
  <li>Thing one</li>
  <li>Thing B</li>
  <li>Thing 4</li>
</ul>

My problem is that when I print the document (or render it as a PDF using wkhtmltopdf), sometimes a page break will occur right after the heading, before the paragraph, which looks quite silly.

Is there a way to stipulate that page breaks should be avoided immediately after a header? (I'm not averse to HTML5/CSS3 solutions, if that simplifies things significantly.)

Note: following suggestions, I tried using the CSS property page-break-after: avoid. This doesn't really work in any WebKit or Mozilla based browsers, though.

Since the CSS property page-break-after: avoid doesn't work in any WebKit or Mozilla based browsers, use the page-break-inside: avoid over the heading and an acceptable amount of the text:

CSS

<style type="text/css">
    .nobreak {
        page-break-inside: avoid;
    }
</style>

HTML

<div class="nobreak">
    <h3>Heading!</h3>

    <p>Some things:</p>

</div>

    <ul>
      <li>Thing one</li>
      <li>Thing B</li>
      <li>Thing 4</li>
    </ul>