It is shown in this paper that the appropriate preprocessing of input data may result in an important reduction of Artificial Neural Network (ANN) training time and simplification of its structure, while improving its performance. The ANN is working as a data predictor in a lossless image coder. Its adaptation is done for each coded pixel separately; no initial training using learning image sets is necessary. This means that there is no extra off-line time needed for initial ANN training, and there are no problems with network overfitting. There are two concepts covered in this paper: Replacement of image pixels by their differences diminishes data variability and increases ANN convergence (Concept 1); Preceding ANN by advanced predictors reduces ANN complexity (Concept 2). The obtained codecs are much faster than one without modifications, while their data compaction properties are clearly better. It outperforms the JPEG-LS codec by approximately 10%.