Historically, two different strategies have been proposed for improving steganographic security by allowing each cover element to be modified by +1 or −1 with unequal probabilities: side-informed steganography and methods that cluster the polarity of neighboring changes. In the first strategy, the sender typically uses the knowledge of quantization errors when developing / processing the cover before embedding. In the latter, embedding on disjoint sub-lattices employs heuristic rules to increase the probability that the polarities of neighboring changes align. In this paper, we propose a method for combining both strategies and experimentally show an improvement in empirical security for several types of side information on two datasets when steganalyzing with rich models as well as convolutional neural networks.