Several statistical agencies have started to use multiply-imputed synthetic microdata to create public-use data in major surveys. The purpose of doing this is to protect the confidentiality of respondents’ identities and sensitive attributes, while allowing standard complete-data analyses of microdata. A key challenge, faced by advocates of synthetic data, is demonstrating that valid statistical inferences can be obtained from such synthetic data for non-confidential questions. Large discrepancies between observed-data and synthetic-data analytic results for such questions may arise because of uncongeniality; that is, differences in the types of inputs available to the imputer, who has access to the actual data, and to the analyst, who has access only to the synthetic data. Here, we discuss a simple, but possibly canonical, example of uncongeniality when using multiple imputation to create synthetic data, which specifically addresses the choices made by the imputer. An initial, unanticipated but not surprising, conclusion is that non-confidential design information used to impute synthetic data should be released with the confidential synthetic data to allow users of synthetic data to avoid possible grossly conservative inferences.