It has been established that the addition of amphiphilic diblock copolymers has a boosting effect in bicontinuous microemulsions by decreasing the minimum amount of surfactant needed to solubilize equal volumes of oil and water. The strength of the polymer effect was found to be about twice larger than the theoretical prediction. This discrepancy is explained by confinement. Previous experimental studies always considered large oil and water domains of size d compared to the typical polymer end-to-end radius, R(ee). The ratio of these two parameters R(ee)/d defines the confinement parameter. We investigated the sensitivity of the polymer influence extending the range of confinement. We combined macroscopic observations of the phase behavior with microscopic measurements of the structure by small-angle neutron scattering (SANS). Both results were compared with computer simulations on the basis of the theoretical concept of Helfrich. The simulations predict an enhanced sensitivity of the polymer at medium confinement and a reversed behavior at larger confinement. The higher sensitivity at medium confinement is only slightly visible experimentally, whereas the reversed behavior (antiboosting) is clearly present. Finally, a comparison with homopolymer addition showed a common high confinement behavior for diblock copolymers and for homopolymers.