Selecting just part of chords with shift-drag

I find myself in this situation fairly frequently. I might have a bunch of chords, and want to select just the top few notes of each of the chords, and cut and past those notes to a different staff. (Or even just delete them.)

I can shift drag, which seems to select the notes (see image 1), but then when I release, it selects the whole chords (see image 2). I do know that it's possible to have the kind of selection I want because I can control click each of the note heads individually to build it (see image 3).

Why isn't the default behavior with shift-drag to create a selection of the elements that are highlighted while I'm dragging?