The analysis of low-level or background dominant radioactivity is complicated by the fact that sample net rate of activity above background may be negative, because of random fluctuations. The traditional large sample confidence intervals can contain negative values for the net rate, although we know the net rate is positive. This problem leads to statistically unsound practices such as the reporting of “less than” values when the net value lies below a certain “detectable limit”. In this paper we present two Bayesian analyses of the data which take account of the fact that the net rate is positive, and thus always lead to positive estimates and probability intervals for the true underlying rate. The estimates and intervals are compared with classical results far twenty trial data sets. (C)1982Health Physics Society