Shortcodes are wrapped in paragraph tags

The HTML editor wraps shortcodes in paragraph tags. Apologies if this is a duplicate, I couldn’t find any similar cases.

I’m trying to add shortcodes for some HTML5 tags I want to use. Before I hit Publish/Update, it looks like this:

[aside]
<p>Aside content</p>
[/aside]
<p>More content outside of the aside</p>

After, WordPress stuffs in <p> tags:

<p>[aside]</p>
<p>Aside content</p>
<p>[/aside]</p>
<p>More content outside of the aside</p>

And sure enough, it doesn’t come out of the_content() correctly. This is the output grabbed with wget:

<aside></p>
<p>Aside content</p>
<p></aside>
<p>More content outside of the aside</p>

This is the page grabbed with Firefox. It moves the closing aside tag to the end:

<aside>
<p>Aside content</p>
<p>
</p><p>More content outside of the aside</p>
</aside>

I am at my wit’s end; calling remove_filter(‘the_content’, ‘wpautop’) in functions.php did nothing whatsoever. I noticed the filter shortcode_unautop but it does not seem to work as advertised.

Note that it is the HTML editor that adds the offending <p>s.

Thanks for any support.