Resize an attributed string without changing the font

Is it possible to change the font size of a mutable attributed string without having to reset the font? I've got an attributed string that's displayed in a text view, and I'd like to have the font size decrease when the string gets too big to fit so that it will still fit in the view. I've got everything pretty much working, but the attributed string has substrings that use different fonts, and I can't figure out how to change the font size without also having to reset the font for each substring. Any ideas?