During the early phase of adenovirus infection the promoter-proximal L1 poly(A) site in the major late transcription unit is used preferentially in spite of the fact that the distal L3 poly(A) site is stronger (i.e. it competes better for processing factors and is cleaved at a faster rate, in vitro). Previous work had established that this was due at least in part to the stable binding of the processing factor, CPSF, to the L1 poly(A) site as mediated by specific regulatory sequences. It is now demonstrated that in addition, the L1 poly(A) site has a positional advantage due to its 5' location in the transcription unit. We also show that preferential processing of a particular poly(A) site in a complex transcription unit is dependent on RNA polymerase II. Our results are consistent with recent reports demonstrating that the processing factors CPSF and CstF are associated with the RNA polymerase II holoenzyme; thus, processing at a weak poly(A) site like L1 can be enhanced by virtue of its being the first site to be transcribed.