Conventional statistical single-channel noise reduction methods suffer from bad performance in highly non-stationary environments. In contrast to that, model-based algorithms have the potential to deal with those adverse conditions. In this paper, we focus on codebook-based algorithms which utilize trained codebooks where typical speech and noise spectral shapes are stored. Speech and noise estimates are determined frame for frame independently which allows to deal with highly non-stationary noise. By incorporating memory, the performance can be further improved. In this paper, elaborated models for memory modeling are presented and a preliminary validation is provided.