Recent advances with self-supervised learning have allowed speech recognition systems to achieve state-of-the-art (SOTA) word error rates (WER) while requiring only a fraction of the labeled training data needed by its predecessors. Notwithstanding, while such models achieve SOTA performance in matched train/test conditions, their performance degrades substantially when tested in unseen conditions. To overcome this problem, strategies such as data augmentation and/or domain shift training have been explored. Available models, however, are still too large to be considered for edge speech applications on resource-constrained devices, thus model compression tools are needed. In this paper, we explore the effects that train/test mismatch conditions have on speech recognition accuracy based on compressed self-supervised speech models. In particular, we report on the effects that parameter quantization and model pruning have on speech recognition accuracy based on the so-called robust wav2vec 2.0 model under noisy, reverberant, and noise-plus-reverberation conditions.