In the context of full waveform inversion (FWI), second-order optimization methods, which take into account more precisely the effect of the Hessian such as the quasi-Newton l-BFGS method, have shown superior convergence properties than first-order methods. When using source encoding techniques, the regeneration of the random variables to assemble the sources at each FWI iteration plays a crucial role since it helps to reduce the so-called cross talk noise produced by the encodings. However, it is not clear how to combine the l-BFGS algorithm and encoding methods because, strictly speaking, l-BFGS needs previous iteration estimations, thus prohibiting the regeneration of the code at each iteration. We study how to combine second-order optimization methods with encoding techniques, considering two truncated matrix-free Newton algorithms (Gauss Newton and full Newton) and the l-BFGS algorithm with periodic restarts and we apply our method on the 2004 BP salt model.