A study of identification properties of a Si-Si$\Delta$ E-E telescope exploiting an underdepleted residual-energy detector has been performed. Five different bias voltages have been used, one corresponding to full depletion, the others associated with a depleted layer ranging from 90% to 60% of the detector thickness. Fragment identification has been performed using either the $\Delta$ E-E technique or the Pulse Shape Analysis (PSA). Both detectors are reverse mounted: particles enter from the low field side, to enhance the PSA performance. The achieved charge and mass resolution has been quantitatively expressed using a Figure of Merit (FoM). Charge collection efficiency has been evaluated and the possibility of energy calibration correcti...