[wp-hackers] Adding class to oembedded media?

[Thomas Belknap]

I'm wondering what the hook is that translates oEmbed URLs like YouTube
URLs into embedded media?

The thing is: I have first-line indents in my paras, which is fine in most
cases. But when media gets added to the page like a YouTube video, that too
gets wrapped in a para and of course gets the first line indent. The result
is a video that's out of alignment with the rest of the page.

The reason for wrapping content in paras is well-discussed, so I'm not
looking to change that. But what I would like to be able to do is at least
specify a class for the para so that I can style it. YouTube videos get
placed inside an iframe and are therefore not style-ready by themselves.