This article proposes a memory-saving decomposition of the design matrix to facilitate the estimation of a linear model with two high-dimensional fixed effects. A common way to fit such a model is to take into account one of the effects by including dummy variables and to sweep out the other effect by the within transformation (fixed-effects transformation). If the number of panel units is high, creating and storing the dummy variables can involve prohibitively large computer-memory requirements. The memory-saving procedure to set up the moment matrices for estimation presented in this article can reduce the memory requirements considerably. The companion Stata ado-file felsdvreg implements the estimation method, takes care of identification issues, and provides useful summary statistics.