In parentage testing using DNA markers, the formulae for calculating the probability of exclusion generally overstate the power of a test battery by considering its ability to exclude a random man. It is known that in many cases, in particular immigration applications, the false father is more likely to be a relative, e.g. brother, of the true father than an unrelated man. This work presents formulae that take this consideration into account. A practical example using Hong Kong data is provided to illustrate the effect of the modification. Also discussed is how the expected efficacy of a test battery will be affected when possible mutations and null alleles or genetic inconsistencies are taken into consideration.