This paper presents new elimination rules for the single machine problem with general earliness and tardiness penalties subject to release dates. These rules, based on a Lagrangian decomposition, allow to drastically reduce the execution windows of the jobs. We measure the efficiency of these properties by integrating them in a branch-and-bound. Tests show that instances with up to 70 jobs without release dates, and up to 40 jobs with release dates, can be optimally solved within 1000 seconds.