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.