The JumpSport is the rebounder that has adjustable bungee cords. I urge people to try this at Costco before buying to make sure you want it. Check with your local Costco to see if they have them on display.
Many people don't want a bungee rebounder that only has one tensile strength so this is the model that I like that is adjustable so a really heavy person can adjust the weight after a very lightweight person was on it. It only takes a few minutes to adjust each cord.
I like the smaller models better as they pronate less unless I am on the larger Jumpsport bungee rebounder and I have the tension up high. Each Jumpsport cords has 7 different tensile levels. The frame is a very high quality (15 gauge steel frame). If sensitive to smell I would get polymer feet and switch them out from the rubber feet. Or if the polymer feet don't fit a model you have and you aren't comfortable with the rubber smell the things you put under a table on a rug can be put under it too but you have to put them on each time you move the rebounder.
I still like the bounce of latex that the Bellicon has but if concerned about sweating on the cords the Jumpsport cords hold up much better. Latex is more expensive and most natural. Latex also has no off gassing which those with chemical sensitivities usually prefer.