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Larger Spiking Neural Network (SNN) models are typically favorable as they can offer higher accuracy. However, employing such models on the resource- and energy-constrained embedded platforms is inefficient. Towards this, we present a tinySNN framework that optimizes the memory and energy requirements of SNN processing in both the training and inference phases, while keeping the accuracy high. It is achieved by reducing the SNN operations, improving the learning quality, quantizing the SNN parameters, and selecting the appropriate SNN model. Furthermore, our tinySNN quantizes different SNN parameters (i.e., weights and neuron parameters) to maximize the compression while exploring different combinations of quantization schemes, precision levels, and rounding schemes to find the model that provides acceptable accuracy. The experimental results demonstrate that our tinySNN significantly reduces the memory footprint and the energy consumption of SNNs without accuracy loss as compared to the baseline network. Therefore, our tinySNN effectively compresses the given SNN model to achieve high accuracy in a memory- and energy-efficient manner, hence enabling the employment of SNNs for the resource- and energy-constrained embedded applications.