In the present invention, viruses, plasmids or both are constructed which contain viral DNA and lox sites positioned such that site-specific recombination between lox sites in separate plasmids results in generation of infectious viral DNA at high-efficiency in cotransfected host cells that have been engineered to express the Cre recombinase. Because of the high-efficiency and specificity of the Cre enzyme, suitably engineered plasmids can be readily recombined to produce infectious virus at high-efficiency in cotransfected 293 cells, without, at the same time, producing wild-type adenovirus, with the attendant problems for removal thereof. Use of recombinases besides Cre and recombinase recognition sites besides lox sites, and use of cells other than 293 cells are also disclosed and enabled, as are kits incorporating the site-specific vector system.