Quantitative analysis of nitrocellulose filter binding data by the method of Clore, Gronenborn and Davies [(1982) J. Mol. Biol. 155, 447-466] has been used to show that lambda integration protein (Int) exhibits cooperativity in binding to specific recognition sites within the attachment site region (lambda attP) of bacteriophage lambda DNA. Optimal values of the equilibrium constant obtained were 3.0(+/- 1.0) X 10(10) M-1 for the P' site using a model of three sites with equal affinity and 1.9(+/- 0.4) X 10(10) M-1 for the P1 site on a two-site model. The value of the cooperativity parameter alpha is 172(+106)(-66) in all cases. The occurrence of a consensus recognition sequence is necessary but not sufficient for strong binding; cooperative interaction between Int molecules binding to adjacent members of an array of binding sites is also essential. The occurrence of binding site arrays distinguishes lambda attP very clearly from other DNA sequences containing single recognition sites by chance.