It has previously been observed that the only specific requirement for transcriptional initiation on viral RNA in vitro by the RNA-dependent RNA polymerase (RdRp) of turnip yellow mosaic virus is the CCA at the 3′ end of the genome. We now compare the abilities of this RdRp, turnip crinkle virus RdRp, and Qβ replicase, an enzyme capable of supporting the complete viral replication cycle in vitro, to transcribe RNA templates containing multiple CCA boxes but lacking specific viral sequences. Each enzyme is able to initiate transcription from several CCA boxes within these RNAs, and no special reaction conditions are required for these activities. The transcriptional yields produced from templates comprised of multiple CCA or CCCA repeats relative to templates derived from native viral RNA sequences vary between 2:1 and 0.1:1 for the different RdRps. Control of initiation by such redundant sequences presents a challenge to the specificity of viral transcription and replication. We identify 3′-preferential initiation and sensitivity to structural presentation as two specificity mechanisms that can limit initiation among potential CCA initiation sites. These two specificity mechanisms are used to different degrees by the three RdRps. The finding that three viral RdRps representing two of the three supergroups within the positive-strand RNA viral RdRp phylogeny support substantial transcription in the absence of unique promoters suggests that this phenomenon may be common among positive-strand viruses. A framework is presented arguing that replication of viral RNA in the absence of unique promoter elements is feasible.