The present invention provides for methods for discriminating between alleles at polymorphic positions in a genome. In general, the methods employ allele-specific extension of oligonucleotides that are complementary to one of the alleles at the 3′ end of the oligonucleotide. The allele-specific oligonucleotides are resistant to proofreading activity from a polymerase and may be extended in an allele-specific manner by a DNA polymerase with a functional 3′ to 5′ exonuclease activity. The allele-specific oligonucleotides may be attached to a solid support such as a chip or a bead.