Experiments show that a ligand-receptor complex formed by binding a bivalent ligand (D) in which the two ligating units are joined covalently by a flexible polymeric spacer (S) can be orders of magnitude more stable than the corresponding complex formed with monomeric ligands. Although molecular models rationalizing this "enhancement effect" have been proffered, they ignore spacer-receptor (S-R) interactions, which can substantially influence the relative stability of complexes. Here, the results of a computational study designed to assess the impact of S-R interactions in the prototypic bivalent complex are presented and compared to results of experiments. The S-R interactions mimicking general features of biological systems are modeled by contoured R surfaces with hills (or depressions) at the binding sites. In the fictitious limit of vanishing S-R interactions, the enhancement is pronounced, as observed in experiments. For strictly repulsive S-R interactions (hard R surface), the enhancement vanishes, or even reverses. This is particularly the case if the R surface is convex (i.e., rising between the binding sites), while the enhancement is only moderately reduced if the R surface is concave. Alternatively, a weak S-R attraction close to the R surface can increase the enhancement. It is concluded that large enhancement should be observed only if both features are present: a concave R surface plus a weak S-R attraction. The latter occurs for spacer material such as polyethylene glycol (PEG), which is weakly hydrophobic and thus attracted by protein surfaces. It is shown that the enhancement of bivalent binding can be characterized by a single key parameter, which may also provide guidelines for the design of multivalent complexes with large enhancement effect.