Speech-based image retrieval has been studied as a proxy for joint representation learning, usually without emphasis on retrieval itself. As such, it is unclear how well speech-based retrieval can work in practice -- both in an absolute sense and versus alternative strategies that combine automatic speech recognition (ASR) with strong text encoders. In this work, we extensively study and expand choices of encoder architectures, training methodology (including unimodal and multimodal pretraining), and other factors. Our experiments cover different types of speech in three datasets: Flickr Audio, Places Audio, and Localized Narratives. Our best model configuration achieves large gains over state of the art, e.g., pushing recall-at-one from 21.8% to 33.2% for Flickr Audio and 27.6% to 53.4% for Places Audio. We also show our best speech-based models can match or exceed cascaded ASR-to-text encoding when speech is spontaneous, accented, or otherwise hard to automatically transcribe.