Image codecs are typically optimized to trade-off bitrate vs. distortion metrics. At low bitrates, this leads to compression artefacts which are easily perceptible, even when training with perceptual or adversarial losses. To improve image quality and remove dependency on the bitrate we propose to decode with iterative diffusion models. We condition the decoding process on a vector-quantized image representation, as well as a global image description to provide additional context. We dub our model `PerCo'' for ``perceptual compression'', and compare it to state-of-the-art codecs at rates from 0.1 down to 0.003 bits per pixel. The latter rate is more than an order of magnitude smaller than those considered in most prior work, compressing a 512x768 Kodak image with less than 153 bytes. Despite this ultra-low bitrate, our approach maintains the ability to reconstruct realistic images. We find that our model leads to reconstructions with state-of-the-art visual quality as measured by FID and KID. As predicted by rate-distortion-perception theory, visual quality is less dependent on the bitrate than previous methods.