The best examples of halo nuclei, exotic systems with a diffuse nuclear cloud surrounding a tightly bound core, are found in the light, neutron-rich region, where the halo neutrons experience only weak binding and a weak, or no, potential barrier. Modern direct-reaction measurement techniques provide powerful probes of the structure of exotic nuclei. Despite more than four decades of these studies on the benchmark one-neutron halo nucleus Be11, the spectroscopic factors for the two bound states remain poorly constrained. In the present work, the Be10(d,p) reaction has been used in inverse kinematics at four beam energies to study the structure of Be11. The spectroscopic factors extracted using the adiabatic model were found to be consistent across the four measurements and were largely insensitive to the optical potential used. The extracted spectroscopic factor for a neutron in an nâ.,"j=2s 1/2 state coupled to the ground state of Be10 is 0.71(5). For the first excited state at 0.32Â MeV, a spectroscopic factor of 0.62(4) is found for the halo neutron in a 1p 1/2 state.