In some embodiments, the amplification method may comprise producing a reaction mix comprising: a nucleic acid sample, a polymerase, nucleotides, a forward primer that hybridizes to a sequence in the bottom strand of a fragment in the sample, and a reverse primer. The reverse primer has a hairpin structure comprising a loop, a stem and a 3′ overhang of at least 8 nucleotides, wherein the 3′ overhang hybridizes to a sequence in the top strand of the fragment. Subjecting the reaction mix at least two rounds of denaturation, renaturation and primer extension conditions results in extension the forward and reverse primers to produce an amplification product that contains: a double stranded region comprising a nick adjacent to the 5′ end of the reverse primer, and the loop of the first hairpin primer. Primer sets and kits for performing the methods are also provided.