I too travel outbound with a carry on but need a checked duffel on the return to hold all the stuff I pick up. I have a couple sizes of folding duffel and won't leave home without one.

I use the Outdoor Products Basic Duffel from Campmor. Comes in sizes from 1150 to 10,600 cu in. I have the 14 x 30 inch (4600 cu in) and it holds a huge amount of stuff yet folds to the size of a dinner plate and about 1/2 inch thick and disappears in your bag outbound. Weight: 10 ounces. It has strong web straps that encircle the bag, not just sewn on, and has rings for a shoulder strap for carrying around and hopping on trains in Europe. Don't let the price fool you, these are very well made duffels. ^

It folds so flat because the fabric is thin but tough nylon, like camping tent or rain jacket material. Any duffel you get with thicker material will take up too much room in your bag as it will not fold so flat. On my trip I grab a cardboard box or two to stiffen it and give it some bulk to handle the baggage conveyors better, and use my clothes as packing, making for a nice light carry on for the return trip. Mine has survived several trips without a scratch but the price is so affordable that if it lasts one trip it has done its job.