The implementation of Deep Convolutional Neural Networks (ConvNets) on tiny end-nodes with limited non-volatile memory space calls for smart compression strategies capable of shrinking the footprint yet preserving predictive accuracy. There exist a number of strategies for this purpose, from those that play with the topology of the model or the arithmetic precision, e.g. pruning and quantization, to those that operate a model agnostic compression, e.g. weight encoding. The tighter the memory constraint, the higher the probability that these techniques alone cannot meet the requirement, hence more awareness and cooperation across different optimizations become mandatory. This work addresses the issue by introducing EAST, Encoding-Aware Sparse Training, a novel memory-constrained training procedure that leads quantized ConvNets towards deep memory compression. EAST implements an adaptive group pruning designed to maximize the compression rate of the weight encoding scheme (the LZ4 algorithm in this work). If compared to existing methods, EAST meets the memory constraint with lower sparsity, hence ensuring higher accuracy. Results conducted on a state-of-the-art ConvNet (ResNet-9) deployed on a low-power microcontroller (ARM Cortex-M4) validate the proposal.