Getting Preview to open .pdfs at last resizing

Let's say I open a .pdf doc. It opens with a way-too-big window. I drag the corner of the window to the (smaller) size I like. I want to be able to close the .pdf and the next time I open it, have Preview remember the last size of the window for that particular doc, and open it the way I left it.

I tried saving the .pdf in the newly-resized window, with no luck. And I didn't see any Preferences that addressed this issue.