In optoacoustic tomography, detectors with relatively large areas are often employed to achieve high detection sensitivity. However, spatial-averaging effects over large detector areas may lead to attenuation of high acoustic frequencies and, subsequently, loss of fine features in the reconstructed image. Model-based reconstruction algorithms improve image resolution in such cases by correcting for the effect of the detector’s aperture on the detected signals. However, the incorporation of the detector’s geometry in the optoacoustic model leads to a significant increase of the model matrix memory cost, which hinders the application of inversion and analysis tools such as singular value decomposition (SVD). We demonstrate the use of the wavelet-packet framework for optoacoustic systems with finite-aperture detectors. The decomposition of the model matrix in the wavelet-packet domain leads to sufficiently smaller model matrices on which SVD may be applied. Using this methodology over an order of magnitude reduction in inversion time is demonstrated for numerically generated and experimental data. Additionally, our framework is demonstrated for the analysis of inversion stability and reveals a new, nonmonotonic dependency of the system condition number on the detector size. Thus, the proposed framework may assist in choosing the optimal detector size in future optoacoustic systems.