A method for preparing a library of one or more target nucleic acid sequences present in a sample at low frequency comprising: amplifying within a single amplification reaction mixture a multiplex of different target sequences from a sample including a plurality of different target sequences, wherein the amplifying includes contacting at least a portion of the sample with a plurality of target-specific primers, and a polymerase under amplification conditions, thereby producing a multiplex of different amplified target sequences, wherein at least two of the plurality of target-specific primers include cleavable groups and at least one of the produced multiplex of different amplified target sequences include cleavable groups at both ends of resulting amplicon, and wherein at least one of the plurality of target specific primers is a blocking primer that does not include the cleavable groups and at least one of the produced multiplex of different amplified target sequences includes a cleavable group at only one end of resulting amplicon; cleaving the cleavable groups of the multiplex of different amplified target sequences and forming cleaved ends; and ligating at least two adapters to cleaved ends of at least one of the multiplex of different amplified target sequences, thereby producing one or more adapter-ligated amplified target sequences; thereby preparing a library of different adapter-ligated target sequences, wherein amplicon ends resulting from blocking primers are not capable of ligating adapter, and wherein none of the adapters in the ligation reaction hybridizes under high stringency conditions to any one of the multiplex of different amplified target sequences. amplifying within a single amplification reaction mixture a multiplex of different target sequences from a sample including a plurality of different target sequences, wherein the amplifying includes contacting at least a portion of the sample with a plurality of target-specific primers, and a polymerase under amplification conditions, thereby producing a multiplex of different amplified target sequences, wherein at least two of the plurality of target-specific primers include cleavable groups and at least one of the produced multiplex of different amplified target sequences include cleavable groups at both ends of resulting amplicon, and wherein at least one of the plurality of target specific primers is a blocking primer that does not include the cleavable groups and at least one of the produced multiplex of different amplified target sequences includes a cleavable group at only one end of resulting amplicon; cleaving the cleavable groups of the multiplex of different amplified target sequences and forming cleaved ends; and ligating at least two adapters to cleaved ends of at least one of the multiplex of different amplified target sequences, thereby producing one or more adapter-ligated amplified target sequences; thereby preparing a library of different adapter-ligated target sequences, wherein amplicon ends resulting from blocking primers are not capable of ligating adapter, and wherein none of the adapters in the ligation reaction hybridizes under high stringency conditions to any one of the multiplex of different amplified target sequences.