Résumé : Register saturation (RS) is the exact maximal register need of all valid schedules of a data dependence graph \cite{Touati:RSILP05}. Its optimal computation is NP-complete. This report proposes two variants of heuristics for computing the acyclic RS of directed acyclic graphs (DAG). The first one improves the previous greedy-k heuristic \cite{Touati:RSILP05} in terms of approximating the RS with equivalent computation times. The second heuristic is faster, has better RS approximation than greedy-k, but scarifies the computation of saturating values. In order to evaluate the efficiency of these two heuristics, we designed an optimal combinatorial algorithm computing the optimal RS for tractable cases, which turns out to be satisfactory in practice. Extensive experiments have been conducted on thousands of data dependence graphs extracted from FFMPEG, MEDIABENCH, SPEC2000 and SPEC2006 benchmarks. Numerical results are presented to demonstrate the efficiency of the two proposed heuristics, so hence they can replace the greedy-k heuristic presented in \cite{Touati:RSILP05}. Our RS computation methods are distributed as a C independent library (\texttt{RSlib}) under LGPL licence.