Interactions between RNA polymerases (RNAP) resulting from tandem or convergent arrangements of promoters can cause transcriptional interference, often with important consequences for gene expression. However, it is not known what factors determine the magnitude of interference and which mechanisms are likely to predominate in any situation. We therefore developed a mathematical model incorporating three mechanisms of transcriptional interference in bacteria: occlusion (in which passing RNAPs block access to the promoter), collisions between elongating RNAPs, and "sitting duck" interference (in which RNAP complexes waiting to fire at the promoter are removed by passing RNAP). The predictions of the model are in good agreement with a recent quantitative in vivo study of convergent promoters in E.coli. Our analysis predicts that strong occlusion requires the interfering promoter to be very strong. Collisions can also produce strong interference but only if the interfering promoter is very strong or if the convergent promoters are far apart (>200 bp). For moderate strength interfering promoters and short inter-promoter distances, strong interference is dependent on the sitting duck mechanism. Sitting duck interference is dependent on the relative strengths of the two promoters. However, it is also dependent on the "aspect ratio" (the relative rates of RNAP binding and firing) of the sensitive promoter, allowing promoters of equal strength to have very different sensitivities to transcriptional interference. The model provides a framework for using transcriptional interference to investigate various dynamic processes on DNA in vivo.