Good threads should never die! I've been meaning to post pics as I promised of how I hold a "barber style" strop. Upon suggestion of Alan Davis a long time ago, my inspiration is straight out of one of the barber's manuals (thanks Alan).
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I like holding these types of strops (I prefer the "barber style) this way because I can make adjustments to the surface of the strop and its flatness, keeping it flat, by pinching with my thumb and index finger and pressing my fingers on the underside of the strop toward my palm. It's hard to describe but easy to see when you hold the strop this way.
Chris L