Future observations of cosmic sources of gamma‐ray lines will require instruments with sensitivities of the order of 10−6photons/cm2‐s. To achieve this sensitivity, external background can be reduced by placing the Ge detector array inside a thick active shield, but the internal background produced by beta decay in the detector must be rejected by the Ge detector itself. In a colloboration between the High Energy Astrophysics Group at JPL and the Semiconductor Spectrometer Team at Lawrence Berkeley Laboratory (LBL), externally segmented coaxial detectors have been fabricated by dividing the outer electrode into five segments. The segmented detector is operated in a multi‐segment mode to reject internal beta activity by requiring that events interact in two or more segments of the detector to be recorded. In this way, approximately 90% of the beta decays can be rejected, while the efficiency for detecting gamma rays remains high. To verify the operation of the first externally segmented detector, the full‐energy‐peak (FEP) efficiency was measured in this multi‐segment mode as a function of the incident gamma‐ray energy and of the discriminator threshold of the segments. To evaluate the the beta rejection efficiency, the detector was irradiated with neutrons to produce75Ge (t1/2=82.78 min) from neutron capture by74Ge(36.5% of natural Ge) in the detector itself.The beta activation spectra of the detector were then recorded by self counting in a series of measurements. Calculations with the Monte Carlo code ACCEPT were made of the gamma‐ray FEP efficiency and of the beta rejection efficiency of the segmented detector. Thre was good agreement with the laboratory measurements, indicating that the code can be applied with confidence to model the response of more complicated detector configurations and environments.