Rich text (or markdown) without paragraphs

I need something a little richer than text and a little more basic than the Rich Text field type.

I need to be able to put italics (and possibly bold and links) into my “headline” and “subhead” types. Ideally the output from Contentful would look something like…

This is an <i>awesome</i> headline

…without surrounding <h1> or <p> tags. So, more than a plain text field, but less than a rich text or markdown field.

Is this a “solved problem”?