A steganographic method called adjacent bin mapping (ABM) is presented. Firstly, it is applied to 3D geometries by mapping the coordinates within two adjacent bins for data embedding. When applied to digital images, it becomes a kind of LSB hiding, namely the LSB + algorithm. In order to prevent the detection using a metric named histogram tail, the hiding is performed in a pseudorandom order. Then we show that the steganalytic algorithms based on histogram characteristic function (HCF) can be prevented by implementing the LSB + algorithm on subsets of pixels having the same neighbor values. The experimental results show that important high-order statistics of the cover image are preserved in this way while little distortion is introduced to 3D geometric models with an appropriate bin size.