Is any way of finding an element more efficient than another?

Is any way of finding an element more efficient than another?

Since jQuery parses the entire dom first, is there any efficiency gain in directing it via the entire CSS chain rather than directly to an ID? That is, if I have a Div with an ID of "foo" and it contains a P with an ID of "bar", is there any speed advantage in using $(div#foo p#bar) as opposed to just using $(p#bar), assuming jQuery would be more efficient if it had both indexes?