Partially hidden Markov models (PHMMs) have previously been introduced. The transition and emission/output probabilities from hidden states, as known from the HMMs, are conditioned on the past. This way, the HMM may be applied to images introducing the dependencies of the second dimension by conditioning. In this paper, the PHMM is extended to multiple sequences with a multiple token version and adaptive versions of PHMM coding are presented. The different versions of the PHMM are applied to lossless bilevel image coding. To reduce and optimize the model cost and size, the contexts are organized in trees and effective quantization of the parameters is introduced. The new coding methods achieve results that are better than the JBIG standard on selected test images, although at the cost of increased complexity. By the minimum description length principle, the methods presented for optimizing the code length may apply as guidance for training (P)HMMs for, e.g., segmentation or recognition purposes. Thereby, the PHMM models provide a new approach to image modeling.