We propose a model that explains the reduction of T-c due to the pinning of
stripes by planar impurity co-doping in cuprates. A geometrical argument a
bout the planar fraction of carriers affected by stripe pinning leads to a
linear T-c suppression as a function of impurity concentration z. The criti
cal value z, for the vanishing of superconductivity is shown to scale like
T-c(2) in the incompressible stripe regime and becomes universal in the com
pressible regime. Our theory agrees very well with the experimental data in
single- and bilayer cuprates co-doped with Zn, Li, Co, etc.