Focusing on prior criminal histories of offenders, this research discusses the relationship between the histories of an individual and the offender's risk of committing either future murders or serious sexual assaults. After introducing the issue of career criminals, the authors discuss the two specific types of serious criminal offenses discussed in this work as murder and serious sexual assault on an adult female. Data for this study were generated by selecting individuals convicted of murder or of either rape or serious indecent assault of a female-aged 16 years or older, from the years 1995 to 1997, from the Home Office database of convictions and from the Police National Computer. This study focused on 386 offenders convicted of murder and 678 offenders convicted of serious sexual assault, each of which had previous convictions, matched to 2,700 controls. After briefly describing the murders and sexual offenders profiled in this study, the authors discuss those murderers and sexual offenders with previous criminal histories. Focusing on risk factors and relationships in murder, the authors suggest that the variables that emerged as risk factors for the various types of murder were those found to be related to increasing the risk of murder in general. Discussing unusual previous offenses, this paper presents background information on individuals convicted of murder who had less common offenses in their criminal backgrounds. Analyzing the data collected in this study, the researchers found that individuals convicted of murdering a family member had very different risk factors from those of general offenders and that convictions for certain types of offenses increased the relative risk for subsequent convictions for more serious offenses. The authors conclude suggesting that rare and unusual criminal offenses indicate a high and statistically significant likelihood of subsequent serious offending. References and a series of appendices defining serious indecent assault, developing the concept of absolute risk, and developing risk scores of serious offending complete this paper.