We prove that through the analysis of the static, nonlinear system output to an exponential sweep excitation, it is possible to make an easy and informed estimation of memory-length and nonlinearity order parameters, prior to complete identification. The selection of these parameters has been a matter of discussion for many years since most identification techniques require early estimates of those. This work extends the results of previous contributions concerning a constrained set of memory- and order-fading nonlinear systems with diagonal kernels, onto the more general case of memory- and order-fading nonlinear systems that admit a Volterra series representation. A full mathematical formulation of the system output is provided, based on the input. Estimates on the parameters may be obtained by simple inspection on a single, filtered, output to the exponential sweep excitation. This happens to be a projection of the multidimensional, order kernels, as we prove. Examples are provided to evidence the simplicity and reliability of the proposed method.