A new route is described for eliminating chaos in nonlinear oscillators by changing only the shape of a weak nonlinear periodic perturbation and illustrated with the example of the Duffing-Holmes oscillator forced with the Jacobian elliptic function sn. Two techniques are used in the illustration: applying the Melnikov-Holmes analysis, and studying the behavior of the Lyapunov exponent from a simple recursion relation which models an unstable limit cycle. The connection with related previously described routes is also discussed in a general setting.PACS numbers: 05.45.-fb, 05.40.+J During the last decades, new phenomena have appeared from the inclusion of terms modeling periodic perturbations in the equations of nonlinear dissipative systems. The most ubiquitous is chaos [1]. It is also clear at first sight from the literature that it is the harmonic functions which have been overwhelmingly used to model the periodic perturbations. However, these functions are solutions of linear oscillators, and rarely of nonlinear equations. Nature is nonlinear, so we should also take the forcing mechanism to be a nonlinear system since this is the generic situation. In other words, it seems more appropriate to employ periodic functions that are solutions of nonlinear oscillators to construct more realistic perturbations. The simplest functions having this requirement are the Jacobian elliptic functions (JEF) [2]. If one considers polynomials to be the simplest nonlinear extension of linear oscillators, their solutions are known to be given in terms of JEF's. This is the case for the most studied nonlinear integrable oscillators, such as the Duffing or the Helmholtz. Also for nonlinearities in the form of harmonic functions, the pendulum, for instance [3], the solutions are in terms of JEF's. In comparison with the harmonic solutions, the JEF's add a new variable to the parameter space of the system: the elliptic parameter m that is responsible for the shape of the perturbation, i.e., for the temporal rate at which energy is transferred from the excitation mechanism to the system, having fixed the period. This fact leads us to expect new aspects of behavior of the system-unexplored in the harmonic case -when m is varied, the remaining parameters being left constant.In this Letter, we show how by altering solely the shape of a weak external nonlinear modulation, one may pass a dynamical system from a regular to a chaotic state, and vice versa. That suggests a possible explanation of some proposed mechanisms for controlling chaos. From previous work on the possibility of eliminating or reducing chaos in a dynamical system [4,5], it seems that the resonant property of the harmonic perturbation causing the regularization of the system is a necessary condition for a complete regularization. In particular, this is the case for the modelwhere asin(pcot) is responsible for the disappearance of chaos when a and p are suitably chosen-starting from chaos at a=0. [See Ref. [4] where /(x,x)=sinx + Gx-/; G,I constants.] The resonance condit...