A method includes creating a stream of uniquely-addressed mail pieces on a web offset press by printing on sections of a web, separating the sections of the web, and printing unique address information on each section of the press-printed material. The unique address is printed by a variable printer according to a mail file of intended recipients. The stream of uniquely-addressed mail pieces is conveyed in a shingled formation. An on-press conversion of the stream of uniquely-addressed mail pieces into a plurality of batches of stacked mail pieces is performed, each batch containing only mail pieces belonging to a common mail delivery group. The on-press conversion includes controlling via the controller the creation of batch separation points among the mail pieces according to the mail file, conveying the stream of mail pieces in the shingled formation into a stacking device, and stacking the mail pieces with the stacking device.