The Galvin-Mycielski-Solovay theorem confirms a conjecture of Prikry saying that a set of reals is strong measure zero if and only if it can be translated away from each meager set. This connection gives rise to a variety of new "notions of smallness", among them the notion of strongly meager where meager is replaced by null in the translation characterization. In my talk, however, I will focus on another variant based on the Marczewski null ideal which is connected to Sacks forcing. In order to further explore the situation, I will introduce the notion of Sacks dense ideals, that is, translation-invariant sigma-ideals dense in Sacks forcing.