This paper proposes an impedance-based design methodology for cylindrical sandwich shells, with the aim to improve the sound transmission loss properties near the ring and coincidence frequency regions. The approach enables to systematically address the poor acoustic performance, characteristic of these problematic frequency regions, while retaining the mechanical properties of these structures. This is done by seeking to suppress the mass-controlled region in the frequency spectrum, with properly tuned characteristic frequencies of the structure, completed by a degree of damping treatment. The impedance-based approach allowing this tuning is derived from the canonical wave equation with a view to sound transmission through cylindrical shells. In addition to offering fast, early design possibilities, the method provides physical insights into the vibroacoustic performance of the shell, for instance introduced to estimate the sound transmission loss of shallow curved sandwich panels in the low-frequency range. Oblique-and diffuse-field conditions are investigated, validating the analytical developments against finite element calculations.