Diploid (2n = 2× = 24) potato (Solarium) species that produce 2n gametes are being utilized in potato breeding programs. Three breeding schemes involving these diploids are presently used by potato breeders to transfer this genetic material from diploid parents to their tetraploid offspring. Derived tetraploids may arise through tetraploid × diploid, tetraploid × haploid-species, or diploid × diploid hybridizations. The inbreeding coefficient of derived tetraploids is a complex function of the coancestry of the parents, the inbreeding of the parents, the coefficient of double reduction in the tetraploid parent, and the frequency of single exchange tetrads in the diploid parent(s), and it depends on the mechanism of 2n gamete formation. For the two breeding strategies involving tetraploid female parents, there is less inbreeding in the derived tetraploid from a diploid parent producing 2n pollen by first division restitution than 2n pollen by second division restitution when the frequency of single exchange tetrads in the diploid is less than 2/3. In bilateral sexual polyploidization, the inbreeding coefficient of a derived tetraploid for a given set of parents from a first division × first division restitution cross is less than the inbreeding coefficient of a second division × first division restitution cross which is less than the inbreeding coefficient of a second division × second division cross when the frequency of single exchange tetrads is less than 2/3.