A method for enriching a target nucleic acid sequence in an amplification reaction mixture, said method comprising: a. providing a primer pair capable of annealing to a reference sequence and also to one or more target sequences that are at least 50% homologous to said reference sequence; b. preparing an amplification reaction mixture including at least the following constituents: a nucleic acid sample having the reference sequence and also suspected of having the one or more target sequences that are at least 50% homologous to said reference sequence and are also amplifiable by the primer pair, and an excess amount of reference blocking sequence relative to the amount of reference sequence, the reference blocking sequence being fully complementary with at least a portion of the sequence of one of the strands of the reference sequence between its primer sites; c. increasing the temperature of the reaction mixture suspected of having said target sequence to a first denaturing temperature that is above the melting temperature (T m) of the reference sequence and above the melting temperature (T m) of the target sequence so as to form denatured reference strands and denatured target strands; d. reducing the temperature of the reaction mixture so as to permit formation of duplexes of the reference blocking sequence and the complementary reference strand and heteroduplexes of the reference blocking sequence and target strands; e. increasing the temperature of said reaction mixture to a critical temperature (T c) sufficient to permit preferential denaturation of said heteroduplexes of the reference blocking sequence and target strands in preference to denaturation of the duplexes of the reference blocking sequence and reference strands; f. reducing the temperature of the reaction mixture so as to permit said primer pair to anneal to the single stranded target strands and any single stranded reference strands in the reaction mixture; and g. extending said primer pair so as to enrich said target sequence relative to said reference sequence; h. repeating steps c through g for two or more cycles in order to enrich said target sequence relative to said reference sequence. a. providing a primer pair capable of annealing to a reference sequence and also to one or more target sequences that are at least 50% homologous to said reference sequence; b. preparing an amplification reaction mixture including at least the following constituents: a nucleic acid sample having the reference sequence and also suspected of having the one or more target sequences that are at least 50% homologous to said reference sequence and are also amplifiable by the primer pair, and an excess amount of reference blocking sequence relative to the amount of reference sequence, the reference blocking sequence being fully complementary with at least a portion of the sequence of one of the strands of the reference sequence between its primer sites; a nucleic acid sample having the reference sequence and also suspected of having the one or more target sequences that are at least 50% homologous to said reference sequence and are also amplifiable by the primer pair, and an excess amount of reference blocking sequence relative to the amount of reference sequence, the reference blocking sequence being fully complementary with at least a portion of the sequence of one of the strands of the reference sequence between its primer sites; c. increasing the temperature of the reaction mixture suspected of having said target sequence to a first denaturing temperature that is above the melting temperature (T m) of the reference sequence and above the melting temperature (T m) of the target sequence so as to form denatured reference strands and denatured target strands; d. reducing the temperature of the reaction mixture so as to permit formation of duplexes of the reference blocking sequence and the complementary reference strand and heteroduplexes of the reference blocking sequence and target strands; e. increasing the temperature of said reaction mixture to a critical temperature (T c) sufficient to permit preferential denaturation of said heteroduplexes of the reference blocking sequence and target strands in preference to denaturation of the duplexes of the reference blocking sequence and reference strands; f. reducing the temperature of the reaction mixture so as to permit said primer pair to anneal to the single stranded target strands and any single stranded reference strands in the reaction mixture; and g. extending said primer pair so as to enrich said target sequence relative to said reference sequence; h. repeating steps c through g for two or more cycles in order to enrich said target sequence relative to said reference sequence.