We present a detailed analysis of a regression and an equivalent band-sharing technique for estimating mean within-group relatedness from DNA fingerprint data. First, we show that the relatedness estimate obtained from this technique tends to underestimate the pedigree relatedness in random-mating populations, but that the degree of underestimation will be small unless DNA fingerprint similarity among unrelated individuals is unusually high. We derive the exact asymptotic downward bias as a function of allele frequency and probabilities of identity by descent. We suggest some methods for removing the small downward bias in the regression estimate. Secondly, we show that the technique yields accurate estimates of parent-offspring, full, and half-sibling relatedness in natural populations of the red-winged blackbird Agelaius phoeniceus and indigo bunting Passerina cyanea.