Described herein are synthetic methods for producing sequence-specific RNA oligonucleotides that eliminate impurities produced in prior art methods. In one aspect, an end-protected capture DNA complementary to a portion of the product RNA is employed. In another aspect, the template DNA is covalently or noncovalently linked to the RNA polymerase, either directly or through the use of a nontemplate DNA. In a third aspect, a flow chamber is employed. All of the methods can be used in combination.