In most countries census data are recognized as being fallible, i.e., subject to various errors of undercounting and erroneous enumeration. Part of the difficulty faced by statistical agencies is that the public tends to think of the census as an exercise in counting. When the census process is more properly viewed as one of estimation then the statistical issues come to the fore, including bias-variance tradeoffs. This paper reconsiders the methodology used in the 1990 and 2000 U.S. decennial censuses to correct for census error through adjustment, namely the post-enumeration survey. The 2000 post-enumeration Accuracy and Coverage Evaluation (ACE) survey re-measured the census results for over 300,000 households in approximately 11,000 blocks nationwide. In March of this year, the U.S. Bureau of the Census made a decision not to adjust the 2000 census using the results of ACE. We review some of the quality considerations surrounding that decision, implications for censuses in other countries, and some related estimation problems growing out of the use of multiple lists.