A granular damper consists in a container partially filled with solid particles that attenuate vibrations thanks to the multiple dissipative particle-particle collisions. These dampers have been investigated for decades because they are affordable, require low maintenance and can operate in harsh environments where viscous dampers fail. However, the nonlinear response of granular dampers, which includes chaotic dynamics and sharp transitions in loss factor, makes it difficult to predict their final performance when attached to the primary vibrating structure. To some extent, this has hampered widespread utilization of granular dampers in the industry. We show that a cone-in-cone design of such dampers can lead to an essentially linear response, which is compatible with a simple force law.