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This paper proposes a modified block-adaptive prediction-based neural network scheme for lossless data compression. A variety of neural network models from a selection of different network types, including feedforward, recurrent, and radial basis configurations are implemented with the scheme. The scheme is further expanded with combinations of popular lossless encoding algorithms. Simulation results are presented, taking characteristic features of the models, transmission issues, and practical considerations into account to determine optimized configuration, suitable training strategies, and implementation schemes. Estimations are used for comparisons of these characteristics with the existing schemes. It is also shown that the adaptations of the improvised scheme increases performance of even the classical predictors evaluated. In addition, the results obtained support that the total processing time of the two-stage scheme can, in certain cases, be faster than just using lossless encoders. Findings of the paper may be beneficial for future work, such as, in the hardware implementations of dedicated neural chips for lossless compression.