Optoacoustic tomography (OAT) has recently been advanced toward ultrafast volumetric imaging frame rates in the kilohertz range. As a result, excessive data processing and storage capacity requirements are increasingly being imposed on the imaging systems. OAT data commonly exhibit significant sparsity across the spatial, temporal or spectral domains, which facilitated the development of compressed sensing algorithms exploiting various sparse acquisition and under-sampling schemes to reduce data rates. However, performance of compressed sensing critically depends on a priori knowledge on the type of acquired data and/or imaged object, commonly resulting in lack of general applicability and unpredictable image quality. In this work, we report on a fast adaptive OAT data compression framework operating on fully sampled tomographic data. It is based on a wavelet packet transform that maximizes the data compression ratio according to the desired signal energy loss. A dedicated reconstruction method was further developed that efficiently renders images directly from the compressed data. Up to 1000x compression ratios were achieved while providing efficient control over the resulting image quality from arbitrary datasets exhibiting diverse spatial, temporal and spectral characteristics. Our approach enables faster and longer acquisitions and facilitates long-term storage of large OAT datasets.