The investigative steps used by a number of existing restitution programs to determine victim losses are applied to a national sample of crime victimizations collected by the National Crime Survey (NCS) for the following crimes: unarmed robbery, purse snatching/pocket picking, household burglary, larceny from the home, larceny elsewhere, and vehicle theft. The report discusses the possible effects on such a program of factors such as offenders' ability to pay, the low wages paid to incarcerated offenders, the fact that many crimes reported to the NCS are not reported to the police, the low arrest rates for those that are reported, and the very low conviction rates for those that are arrested. The report concludes that relatively few single victimizations are so costly as to prohibit the possibility of restitution, even considering the low earnings of most offenders, but that restitution can be expected to restore the losses for only a very small minority of victims. A broad program of victim compensation must rely on other remedies. The report also discusses the history and background of restitution, with a list of references, and includes 10 tables and 2 figures displaying national estimates of loss, damage, recovery, inmate income, and arrest rates. The investigative steps covered include type of loss (theft, damage, medical expense, lost work time), gross amounts lost, police recovery, insurance payments, net loss, earning capacity of offenders, and victims' relative financial needs. (Author abstract modified).