To hide information within a picture we usually replace the least significant bits. This approach is no longer available if there is only 1 bit/pixel like for Quick Response Codes we meet everyday now. I will talk about theoretical limitation and practical aspects of hiding information in such situations: by generating encoding sequences fulfilling given constraints, for example to enforce resemblance to given picture (grayness of pixel defines probability of using "1" there). If the receiver would know the constraints/picture, we could just use entropy coder for this purpose, but we would like to omit this requirement here. In Kuznetsov-Tsybakov problem only the sender knows simple constraints, but it turns out that we can approach the same channel capacity as if both sides would know them. I will talk about generalizations to statistical constraints and applications for example to picture codes, steganography or lossy compression.