In low bit-rate coders, the near-sample and far-sample redundancies of the speech signal are usually removed by a cascade of a shortterm and a long-term linear predictor. These two predictors are usually found in a sequential and therefore suboptimal approach. In this paper we propose an analysis model that jointly finds the two predictors by adding a regularization term in the minimization process to impose sparsity constraints on a high order predictor. The result is a linear predictor that can be easily factorized into the short-term and long-term predictors. This estimation method is then incorporated into an Algebraic Code Excited Linear Prediction scheme and shows to have a better performance than traditional cascade methods and other joint optimization methods, offering lower distortion and higher perceptual speech quality.