Spike-based neuromorphic hardware promises to reduce the energy consumption of image classification and other deep learning applications, particularly on mobile phones or other edge devices. However, direct training of deep spiking neural networks is difficult, and previous methods for converting trained artificial neural networks to spiking neurons were inefficient because the neurons had to emit too many spikes. We show that a substantially more efficient conversion arises when one optimizes the spiking neuron model for that purpose, so that it not only matters for information transmission how many spikes a neuron emits, but also when it emits those spikes. This advances the accuracy that can be achieved for image classification with spiking neurons, and the resulting networks need on average just two spikes per neuron for classifying an image. In addition, our new conversion method improves latency and throughput of the resulting spiking networks.