Moving constituents can sometimes leave material behind in phase edges they pass through, a phenomenon I term intermediate stranding (IS). IS under A'-movement is subject to restrictions, which I argue provide novel evidence for two concepts: #1: The Cyclic Linearization (CL) theory of successive-cyclic movement (Fox & Pesetsky 2005, Ko 2014). #2: A theory of movement as driven by probe-goal Agree (Chomsky 1995, Ko 2014, van Urk 2015) which predicts restricted movement in phrase edges. When combined, these concepts predict a cross-linguistic word order generalization about IS, which I argue is correct: IS under successive-cyclic movement is only possible when the stranded material is, or can be, attached to the right of the material that continues to move leftward.