Steganographic modiﬁcations must not noticeably change characteristics of the cover data known to an attacker. However, it is a diﬃcult task to deﬁne an appropriate set of features that should be preserved. This article investigates possibilities to maintain statistical properties while embedding information. As an example, the simple embedding function “overwriting the least signiﬁcant bits” is discussed, w.r.t. greyscale images used as covers. Two modiﬁcations of this technique are presented here: The ﬁrst modiﬁcation avoids changes of ﬁrst-order statistics and thereby overcomes possible attacks based on histogram analysis.