The computational modeling of peptide inhibitors to target protein-protein binding interfaces is growing in interest as these are often too large, too shallow, and too feature-less for conventional small molecule compounds. Here, we present a rare successful application of an alchemical binding free energy method for the calculation of converged absolute binding free energies of a series of protein-peptide complexes. Specifically, we report the binding free energies of a series of cyclic peptides derived from the LEDGF/p75 protein to the integrase receptor of the HIV1 virus. The simulations recapitulate the effect of mutations relative to the wild-type binding motif of LEDGF/p75, providing structural, energetic and dynamical interpretations of the observed trends. The equilibration and convergence of the calculations are carefully analyzed. Convergence is aided by the adoption of a single-decoupling alchemical approach with implicit solvation, which circumvents the convergence difficulties of conventional double-decoupling protocols. We hereby present the single-decoupling methodology and critically evaluate its advantages and limitations. We also discuss some of the challenges and potential pitfalls of binding free energy calculations for complex molecular systems which have generally limited their applicability to the quantitative study of protein-peptide binding equilibria.