Handling peak amplitude constraints, or equivalently l∞-norm constraints, is an important application demand in experiment design for system identification. The aim of this letter is to present a method for the design of excitation signals with prescribed power spectrum under l∞-norm constraints for systems with many inputs and outputs. The method exploits an exponential smoothing function in an iterative algorithm. Fast convergence is achieved by a computationally efficient construction of the gradient and the Hessian matrix. Experimental results show excellent convergence behavior that overcomes local minima, while significantly reducing computation time compared to existing techniques.