A cost-effective implementation of Convolutional Neural Nets on the mobile edge of the Internet-of-Things (IoT) requires smart optimizations to fit large models into memory-constrained cores. Reduction methods that use a joint combination of filter pruning and weight quantization have proven efficient in searching the compression that ensures minimum model size without accuracy loss. However, there exist other optimal configurations that stem from the memory constraint. The objective of this work is to make an assessment of such memory-bounded implementations and to show that most of them are centred on specific parameter settings that are found difficult to be implemented on a low-power RISC. Hence, the focus is on quantifying the distance to optimality of the closest implementations that instead can be actually deployed on hardware. The analysis is powered by a two-stage framework that efficiently explores the memory-accuracy space using a lightweight, hardware-conscious heuristic optimization. Results are collected from three realistic IoT tasks (Image Classification on CIFAR-10, Keyword Spotting on the Speech Commands Dataset, Facial Expression Recognition on Fer2013) run on RISC cores (Cortex-M by ARM) with few hundreds KB of on-chip RAM. INDEX TERMS Neural networks, Internet of Things, optimization methods, low power electronics.