Then it says: is a big word, but implementations have been pretty good here.

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Well headers are often of larger font-size than body type.

Paragraph tags are block-level, and thus the will break to a new line if they follow an inline element and the effect will not be achieved. If a run-in element precedes a block level element, the run in element will behave structurally as if it has become the block level elements first inline child element. Well it might be because browser support is a bit weird.

You could insert the tag, but that has semantic concerns, and more importantly, long term maintenance concerns. Rumor has it that Mozilla isn't happy with the spec.

In my own reading of the spec, I find it a bit unclear.

Does that mean that there can't be two headers, both run-ins, that run into a paragraph below?

That's how I would read it, but I think the Web Kit implementation where they both fall inside makes more sense. Mind-bending, I know, but current modern browsers are doing good here. There is also a super hardcore demo (which is over 10 years old).

Opera and IE 8 follow the spec in that the first run-in becomes block and the second goes inline. If the run-in element contains anything block-level, it becomes block-level.

Firefox doesn't support it at all, including the version 4 betas.

The Web Kit family (Safari and Chrome) are supporting it, as well as Opera and IE 8.