Methods and compositions are provided for improving specificity during amplification of a target DNA sequence. The methods and compositions rely upon the use of an RNase H enzyme, a polymerase, and RNase H enzyme-sensitive, blocked-cleavable oligonucleotide primers in the amplification reactions, wherein the reaction mixtures include either an optimized final concentration of a divalent metal salt comprising 2.0 mM or less of free Mg++ cation and/or an optimized final concentration of a non-ionic detergent comprising at least about 0.001% polyethylene glycol hexadecyl ether.