The present invention provides methods, compositions, and kits comprising snap-back primers used for forming 3′ hairpin structures, 5′ hairpin structures, and double hairpin structures. The hairpin structures may be used for detecting target sequences (e.g., such as small RNA target sequence), for detecting polymorphisms in target sequences (e.g., such as polymorphisms located near the 5′ or 3′ ends of the target sequence), or other nucleic acid characterization methods. In certain embodiments, the hairpin structures form invasive cleavage structures (e.g., in combination with a probe or upstream oligonucleotide) which may be cleaved by structure-specific enzymes in order to detect the presence or absence of a particular nucleotide or nucleotide sequence.