An accessory structure trampoline has a main trampoline with a main trampoline bed, main trampoline springs, and a main trampoline spring cover. The main trampoline includes trampoline legs having a first vertical leg section and a second vertical leg section. An accessory structure is pivotally mounted to the first vertical leg section and the second vertical leg section. The accessory structure folds from a deployed position to a stowed position. The accessory structure can be a small trampoline that is smaller than the main trampoline. The small trampoline folds from a deployed position to a stowed position. The small trampoline has a fold-down handlebar and folding legs, and the fold-down handlebar folds from a deployed position to a stowed position. The accessory structure can also be a hammock swing. The hammock swing folds from a deployed position to a stowed position.