Signals acquired by optoacoustic tomography systems have broadband frequency content that encodes information about structures on different physical scales. Concurrent processing and rendering of such broadband signals may result in images with poor contrast and fidelity due to a bias towards low frequency contributions from larger structures. This problem cannot be addressed by filtering different frequency bands and reconstructing them individually, as this procedure leads to artefacts due to its incompatibility with the entangled frequency content of signals generated by structures of different sizes. Here we introduce frequency-band model-based (fbMB) reconstruction to separate frequency-band-specific optoacoustic image components during image formation, thereby enabling structures of all sizes to be rendered with high fidelity. In order to disentangle the overlapping frequency content of image components, fbMB uses soft priors to achieve an optimal trade-off between localization of the components in frequency bands and their structural integrity. We demonstrate that fbMB produces optoacoustic images with improved contrast and fidelity, which reveal anatomical structures in in vivo images of mice in unprecedented detail. These enhancements further improve the accuracy of spectral unmixing in small vasculature. By offering a precise treatment of the frequency components of optoacoustic signals, fbMB improves the quality, accuracy, and quantification of optoacoustic images and provides a method of choice for optoacoustic reconstructions.