Results of two experimental campaigns are presented investigating shell structure in neutron-rich nuclei near 54Ca and 132Sn, respectively. In the first experiment excited states in 55Ti were investigated at the middle focus of the GSI FRS via one-neutron knock-out from 56Ti. Longitudinal momentum distributions were measured inclusively and in coincidence with a newly discovered gamma-ray at 955 keV detected by the MINIBALL gamma-ray detector array. From the momentum distributions the νp1/2 single-particle structure of the ground state was determined for the first time while the excited state at 955 keV is identified as the νp3/2 single-particle state. Secondly, results from the Coulomb excitation of neutron-rich nuclei 122,124,126Cd, 138,140,142,144Xe are presented. These experiments were performed at the REX-ISOLDE accelerator at CERN also using the MINIBALL array. The obtained B(E2)-values follow the expected systematic behavior that correlates the energy of the first excited 2+ state with the B(E2)-values and also agree well with the results of theoretical predictions.