We present improved numerical approximations to the exact Poissonian confidence limits for small numbers n of observed events following the approach of Gehrels ( 1986 ) .
Analytic descriptions of all parameters used in the approximations are provided to allow their straightforward inclusion in computer algorithms for processing of large data sets .
Our estimates of the upper ( lower ) Poisson confidence limits are accurate to better than 1 % for n \leq 100 and values of S , the derived significance in units of Gaussian standard deviations , of up to 7 ( 5 ) .
In view of the slow convergence of the commonly used Gaussian approximations toward the correct Poissonian values , in particular for higher values of S , we argue that , for n \leq 40 , Poissonian statistics should be used in most applications , unless errors of the order of , or exceeding , 10 % are acceptable .