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A brain--machine interface (BMI) based on motor imagery (MI) enables the control of devices using brain signals while the subject imagines performing a movement. It plays a vital role in prosthesis control and motor rehabilitation. To improve user comfort, preserve data privacy, and reduce the system's latency, a new trend in wearable BMIs is to execute algorithms on low-power microcontroller units (MCUs) embedded on edge devices to process the electroencephalographic (EEG) data in real-time close to the sensors. However, most of the classification models present in the literature are too resource-demanding, making them unfit for low-power MCUs. This paper proposes an efficient convolutional neural network (CNN) for EEG-based MI classification that achieves comparable accuracy while being orders of magnitude less resource-demanding and significantly more energy-efficient than state-of-the-art (SoA) models for a long-lifetime battery operation. To further reduce the model complexity, we propose an automatic channel selection method based on spatial filters and quantize both weights and activations to 8-bit precision with negligible accuracy loss. Finally, we implement and evaluate the proposed models on leading-edge parallel ultra-low-power (PULP) MCUs. The final 2-class solution consumes as little as 30 uJ/inference with a runtime of 2.95 ms/inference and an accuracy of 82.51% while using 6.4x fewer EEG channels, becoming the new SoA for embedded MI-BMI and defining a new Pareto frontier in the three-way trade-off among accuracy, resource cost, and power usage.