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Incremental learning is useful if an AI agent needs to integrate data from a stream. The problem is non trivial if the agent runs on a limited computational budget and has a bounded memory of past data. In a deep learning approach, the constant computational budget requires the use of a fixed architecture for all incremental states. The bounded memory generates data imbalance in favor of new classes and a prediction bias toward them appears. This bias is commonly countered by introducing a data balancing step in addition to the basic network training. We depart from this approach and propose simple but efficient scaling of past class classifier weights to make them more comparable to those of new classes. Scaling exploits incremental state level statistics and is applied to the classifiers learned in the initial state of classes in order to profit from all their available data. We also question the utility of the widely used distillation loss component of incremental learning algorithms by comparing it to vanilla fine tuning in presence of a bounded memory. Evaluation is done against competitive baselines using four public datasets. Results show that the classifier weights scaling and the removal of the distillation are both beneficial.