Consumer responses to three cost containment strategies for providing health care are examined. The data come from a random sample of 365 Los Angeles adults interviewed by telephone. It is found that aggregate sample responses are negative toward two strategies (labelled preferred provider and health planning) and positive toward the third (labelled self care). Furthermore, it is found that demographic characteristics that predict approval of one strategy predict disapproval of other strategies. These findings, coupled with models assessing how and why segments of consumers respond as they do, suggest that no one strategy is likely to appeal to all consumers. Implications for the implementation of health care delivery systems inspired by containment strategies are discussed in the context of recent events in California.