The Cre/loxP system is widely used as a genetic tool to manipulate DNA. Cre recombinase catalyzes site-specific recombination between 34 bp loxP sites. Each loxP site is recognized by two Cre molecules assuming a cleaving (CreC) and non-cleaving (CreNC) activity. Despite the symmetry in the sequences of the arms of loxP, available biochemical data show strong evidence that the recombination reaction is asymmetric with a preferred strand exchange order. The asymmetry comes from the spacer separating the two sets of palindromic arms of the loxP sequence. However, it remains to be understood how this preferential order is established. We apply computational structure-based methods and perform a thorough detailed analysis of available structural and biochemical information on the Cre/loxP system in order to investigate such asymmetry in the recombination, and we propose a rationale to explain the determinants favoring the strand exchange order. We show that the structural properties of the DNA flanking sequence of the spacer guide the recombination, and we establish the role of residues R118, R121 and K122 from CreC, which contact the spacer region and by clamping the DNA inhibit the cleavage on the second arm of loxP. Our studies give an atomistic insight on the synapsis state of the recombination process in the Cre/loxP system and highlight the importance of the flexibility and other intrinsic properties of the flanking regions of the DNA spacer to establish a preferential strand exchange order.