In the last two decades, great efforts have been made in the development of 3D cadmium-zinc-Telluride (CZT) detectors operating at room temperature for gamma-ray spectroscopic imaging. This work presents the spectroscopic performance of new high-resolution CZT drift strip detectors, recently developed at IMEM-CNR of Parma (Italy) in collaboration with due2lab (Italy). The detectors (19.4 mm × 19.4 mm × 6 mm) are organized into collecting anode strips (pitch of 1.6 mm) and drift strips (pitch of 0.4 mm) which are negatively biased to optimize electron charge collection. The cathode is divided into strips orthogonal to the anode strips with a pitch of 2 mm. Dedicated pulse processing analysis was performed on a wide range of collected and induced charge pulse shapes using custom 32-channel digital readout electronics. Excellent room-Temperature energy resolution (1.3% FWHM at 662 keV) was achieved using the detectors without any spectral corrections. Further improvements (0.8% FWHM at 662 keV) were also obtained through a novel correction technique based on the analysis of collected-induced charge pulses from anode and drift strips. These activities are in the framework of two Italian research projects on the development of spectroscopic gamma-ray imagers (10-1000 keV) for astrophysical and medical applications.