Yes, the thicker strap I have now is perfect. I used this bag exclusively for 7 months (just rotated it out of use for my DE Speedy now that the rains have started). I flew across country 4x with the Josephine GM. Really love the doctor's bag opening for travel. The jacquard is sturdier than I expected, so if I saw any dirt (usually in corners), I would wipe down with some soap and water or a spritz of this great water-based spot remover called Folex. I had been looking for the preloved LV strap and would often see those in navy, not cherry. So, I'd keep an eye out if you want original strap. Enjoy your bag...it really is great and the PM is the perfect size for daily use. My GM is more than I need on a daily basis, but was great when shopping or traveling.