The nonionic surfactant hexa(ethylene glycol) mono-n-dodecyl ether (C12EO6) self-assembles in aqueous solutions to form small globular micelles. Progressive substitution of C12EO6 by a telechelic polymer (a water soluble poly(ethylene oxide) (PEO) chain grafted at both extremities with hydrophobic C12H25 chains (PEO-2m)) is shown to preserve the initial C12 hydrophobic cores, at least up to 10 polymers per hydrophobic core, but to introduce additional interactions between the micelles. At low micellar concentrations (similar to < 0.03 M) these interactions are attractive, leading to a phase separation even with a minute substitution of C12EO6 by the polymer while at higher concentrations even a minute substitution leads to an effective repulsive interaction. These observations are discussed in terms of a competition between bridging and decoration of the micelles.