Danish sperm donors face a particular kind of kinship trouble: they find themselves in a cultural and organizational context that offers different and contrary ways of how to make connections to donor-conceived individuals meaningful. Whereas Danish sperm banks and Danish law want sperm donors to regard these connections as contractual issues, the dominant kinship narrative in Denmark asks sperm donors to also consider them as family and kinship relations. Based on interviews with Danish sperm donors and participant observation at Danish sperm banks, I argue that Danish sperm donors make sense of connections to donor-conceived individuals as a particular kind of relatedness that cannot be reduced to either contractual or kinship relations. Making sense of these connections, sperm donors negotiate their social significance and thereby participate in opening a space which offers avenues for new kinds of sociality.