Efforts to incorporate bioavailability adjustments into regulatory water quality criteria in the United States have included four major procedures: hardness-based single-linear regression equations, water-effect ratios (WERs), biotic ligand models (BLMs), and multiple-linear regression models (MLRs) that use dissolved organic carbon, hardness, and pH. The performance of each with copper (Cu) is evaluated, emphasizing the relative performance of hardness-based versus MLR-based criteria equations. The WER approach was shown to be inherently highly biased. The hardness-based model is in widest use, and the MLR approach is the US Environmental Protection Agency's (USEPA's) present recommended approach for developing aquatic life criteria for metals. The performance of criteria versions was evaluated with numerous toxicity datasets that were independent of those used to develop the MLR models, including olfactory and behavioral toxicity, and field and ecosystem studies. Within the range of water conditions used to develop the Cu MLR criteria equations, the MLR performed well in terms of predicting toxicity and protecting sensitive species and ecosystems. In soft waters, the MLR outperformed both the BLM and hardness models. In atypical waters with pH <5.5 or >9, neither the MLR nor BLM predictions were reliable, suggesting that site-specific testing would be needed to determine reliable Cu criteria for such settings. The hardness-based criteria performed poorly with all toxicity datasets, showing no or weak ability to predict observed toxicity. In natural waters, MLR and BLM criteria versions were strongly correlated. In contrast, the hardness-criteria version was often out of phase with the MLR and, depending on waterbody and season, could be either strongly overprotective or underprotective. The MLR-based USEPA-style chronic criterion appears to be more generally protective of ecosystems than other models.