All RNAPs (RNA polymerases) repeatedly make use of their DNA template by progressing through the transcription cycle multiple times. During transcription initiation and elongation, distinct sets of transcription factors associate with multisubunit RNAPs and modulate their nucleic-acid-binding and catalytic properties. Between the initiation and elongation phases of the cycle, the factors have to be exchanged by a largely unknown mechanism. We have shown that the binding sites for initiation and elongation factors are overlapping and that the binding of the factors to RNAP is mutually exclusive. This ensures an efficient exchange or 'swapping' of factors and could furthermore assist RNAP during promoter escape, enabling robust transcription. A similar mechanism applies to the bacterial RNAP system. The elongation factors are evolutionarily conserved between the bacterial (NusG) and archaeo-eukaryotic (Spt5) systems; however, the initiation factors [σ and TBP (TATA-box-binding protein)/TF (transcription factor) B respectively] are not. Therefore we propose that this factor-swapping mechanism, operating in all three domains of life, is the outcome of convergent evolution.