Enforcement records cannot provide an accurate estimate of crime rates since they also reflect agency resources and priorities. Investigating random samples of persons is an alternative approach which has been used by the Internal Revenue Service (IRS) since its 1948 Audit Control Program. The Taxpayer Compliance Measurement Program (TCMP) established in 1962 expanded the use of this technique, and over 20 TCMP studies have been conducted on different tax areas and years. This paper examined the longest time series of the TCMP surveys which covered the 1963, 1965, 1969, and 1973 tax years and the following types of noncompliance: proportion of returns with tax underreporting errors, the average net tax underreported, and the proportion of total tax liability this underreporting represented. Adjusted TCMP indexes showed that the average amount of tax underreported remained roughly unchanged -- $152 in 1963 and $146 in 1973 -- but the overall underreporting rate increased 40 percent over the 10-year period. Referrals for potential criminal tax evasions were similar throughout the time period and were estimated to average 20 per 10,000 returns. Based on IRS auditing procedures, this would probably translate into 1 to 2 criminal convictions for every 10,000 returns. These data do not include criminal nonfilers or corporate tax offenses. Rates estimated for civil fraud averaged 9 per 10,000, while rates for negligence violations were 123 per 10,000. The low incidence of civil fraud suggests weakness in the TCMP survey design. A vast increase in the audit staff, however, would be required to process additional fraud referrals. In addition, individuals receiving income from business, farm, or a profession had violation rates 5 to 9 times higher than wage earners or salaried individuals. These findings illustrate the potential uses and versatility of the random investigation method, but more research is needed to determine what other types of offenses it is suited to measure. Tables and 9 references are included.