Abstract Site-specific recombination promoted by serine integrases can be used for ordered assembly of DNA fragments into larger arrays. When a plasmid vector is included in the assembly, the circular product DNA molecules can transform E. coli cells. A convenient “one-pot” method using a single integrase involves recombination between pairs of matched orthogonal attachment sites, allowing assembly of up to six DNA fragments. However, the efficiency of assembly decreases as the number of fragments increases, due to accumulation of incorrect products in which recombination has occurred between mismatched sites. Here we use mathematical modelling to analyse published experimental data for the assembly reactions and suggest potential ways to improve assembly efficiency. We assume that unproductive synaptic complexes between pairs of mismatched sites become predominant as the number and diversity of sites increase. Our modelling predicts that the proportion of correct products can be improved by raising fragment DNA concentrations and lowering plasmid vector concentration. The assembly kinetics is affected by the inactivation of integrase in vitro . The model also predicts that the precision might be improved by redesigning the location of attachment sites on fragments to reduce the formation of the wrong circular products. Our preliminary experimental explorations of assembly with ϕC31 integrase confirmed that assembly efficiency might be improved. However, optimization of efficiency would require more experimental work on the mechanisms of wrong product formation. The use of a more efficient integrase (such as Bxb1) might be a more promising approach to assembly optimization. The model might be easily extended for different integrases or/and different assembly strategies, such as those using multiple integrases or multiple substrate structures.