Cell-free hemoglobin (Hb)-based oxygen carriers have long been proposed as blood substitutes but their clinical use remains tricky due to problems of inefficiency and/or toxicity. Conjugation of Hb with the biocompatible polymer poly(ethylene glycol) (PEG) greatly improved their performance. However, physiological data suggested a polymer molecular weight (M-w) threshold of about 10 kDa, beyond which the grafting of two PEG chains no longer improves efficiency and nontoxicity of diPEG/Hb conjugates. We used small-angle neutron scattering and contrast variation, which are the only techniques able to probe separately the conformation of PEG chains and Hb protein within the complex, to investigate the role of PEG chain conformation in diPEGylated Hb conjugates as a function of the polymer M-w. We found out that the structure of Hb tetramer is not modified by the polymer grafting. Similarly, with a constant grafting of two chains per protein, there is no significant change of the Gaussian conformation between free and grafted PEG below similar to 10 kDa, the complex being well described by the dumbbell model. However, beyond that threshold, the radius of gyration of grafted PEG is significantly smaller than that of the free polymer, showing a compaction of the PEG chains, either in the dumbbell model or in the shroud one. In the latter model, the polymer may be wrapped on the surface of the protein spreading a protective shielding effect over a larger fraction of the protein. Both proposed models are in good agreement with the physiological data reported in the literature.