This paper proposes optimal Boolean, stack, and FIR-Boolean hybrid filters for realizing the prediction stage in lossless grey-level image compression. New optimal design procedures for Boolean filters are introduced, where the optimality criterion is the Error Entropy (EE). The use of the EE-optimal and MAE-optimal Boolean and stack filters in the sequential prediction structure is considered, under different instances: global-optimal, block-optimal, adaptive-size-block-optimal and multiresolution. An extensive simulation study is carried out for analyzing and comparing the performances of the newly introduced predictors and various other sequential predictors. The EE-optimal Boolean predictors prove to be the most efficient predictors. More refined filtering structures, such as block-optimal or adaptive-size-block-optimal are suitable for the prediction task when the prediction mask ought to be small. The proposed progressive transmission structure based on optimal Boolean prediction is shown to outperform HINT HINT progressive lossless coding scheme.