Just for a broader perspective on strategies, I've used no padding whatsoever, just have been dropping our Brompton into the B&W case and taking off, no straps no nothing. Over time I ripped a bit the foam that the B&W case comes with and filled the damage with spray-on construction foam - works very well. Even that ripping has been mostly done when I forced our Dahon bikes into the case - they don't fit as well a Brompton.