People can intentionally forget studied material when cued to do so. Corresponding evidence has arisen from studies on item-method directed forgetting, in which participants are asked to forget single items directly upon presentation. We measured memory performance of to-be-remembered (TBR) and to-be-forgotten (TBF) items across retention intervals of up to 1 week and fitted power functions of time to the observed recall (Experiment 1) and recognition (Experiment 2) rates. In both experiments and each retention interval condition, memory performance for the TBR items was higher than for the TBF items, supporting the view that directed forgetting effects are lasting. Recall and recognition rates of both TBR and TBF items were well fit by the power function. However, the relative forgetting rates of the two item types differed, with a higher forgetting rate for the TBF than the TBR items. The findings are consistent with the view that TBR and TBF items differ (mainly) in recruitment of rehearsal processes and resulting memory strength.