Long-range electrostatic interactions are generally assigned a subordinate role in the high-affinity binding of proteins by glycosaminoglycans, the most highly charged biopolyelectrolytes. The discovery of high and low sulfation domains in heparan sulfates, however, suggests selectivity via complementarity of their linear sulfation patterns with protein charge patterns. We examined how charge sequences in anionic/nonionic copolymers affect their binding to a protein with prominent charge anisotropy. Experiments and united-atom Monte Carlo simulations, together with Delphi electrostatic modeling for the protein, confirm strongest binding when polyanion sequences allow for optimization of repulsive and attractive electrostatics. Simulations also importantly identified retention of considerable polyion conformational freedom, even for strong binding. The selective affinity for heparins of high and low charge density found for this protein is consistent with nonspecific binding to distinctly different protein charge domains. These findings suggest a more nuanced view of specificity than previously proposed for heparinoid-binding proteins.