A trampoline provides higher performance and greater shock absorption capability by utilizing pairs of springs to connect the rebounding mat to the supporting frame. The springs in each pair are coupled to a common junction on the periphery of the rebounding mat. The upper spring in each pair is directly connected to the rebounding mat and the trampoline frame to initially to tension the mat in the equilibrium position. The lower spring in each pair is coupled to the frame and then to rebounding mat via a linkage arm such that it comes substantially under tension only as the corresponding upper spring is stretched. Depending on the level of impact force on the trampoline mat both springs extend, such that their combined stored energy propels the user upward on the return bounce. However, as each spring pair engages in stages the shock of the users initially landing is gradually absorbed.