We target the problem of developing new low-complexity networks for the sound event detection task. Our goal is to meticulously analyze the performance-complexity trade-off, aiming to be competitive with the large state-of-the-art models, at a fraction of the computational requirements. We find that low-complexity convolutional models previously proposed for audio tagging can be effectively adapted for event detection (which requires frame-wise prediction) by adjusting convolutional strides, removing the global pooling, and, importantly, adding a sequence model before the (now frame-wise) classification heads. Systematic experiments reveal that the best choice for the sequence model type depends on which complexity metric is most important for the given application. We also investigate the impact of enhanced training strategies such as knowledge distillation. In the end, we show that combined with an optimized training strategy, we can reach event detection performance comparable to state-of-the-art transformers while requiring only around 5% of the parameters. We release all our pre-trained models and the code for reproducing this work to support future research in low-complexity sound event detection at https://github.com/theMoro/EfficientSED.