The sensitivity of the global properties of a turbulent wake behind a D-shaped bluff cylinder is investigated experimentally by introducing a much smaller control cylinder of various shapes and diameters as a local disturbance. Hot-wire anemometry and particle image velocimetry are used to obtain local and global measurements of the turbulent wake. Aerodynamic forces acting on the main cylinder are derived from pressure measurements around its perimeter. The results are presented in the form of sensitivity maps of the Strouhal number and base pressure. The sensitivity of global properties is interpreted on the basis of the ability of the control cylinder to change the size of the formation region of the Kármán vortex street mainly through the turbulent properties modification of the perturbed detached shear layer. The corresponding physical mechanisms are discussed with regard to the origins of drag reduction and global frequency modification. The impact of the perturbation on the 3D properties of the wake is investigated through two-point velocity correlation and wake visualization. Bi-stable flow configurations for some positions of the control cylinder are examined.