Superconducting, magnetic, and non-Fermi-liquid-like ground states evolve i
n CeCu2+xSi2 with small changes in the Ce/Cu ratio that leave the average c
rystal structure unchanged. We find, however, that the local atomic structu
re determined by neutron pair density function analysis for a superconducti
ng sample with x = 0.33 is fundamentally different from a nonsuperconductin
g sample with x = - 0.08. The local lattice of the Cu-deficient sample exhi
bits long-range atomic order, while the Cu-rich sample is intrinsically dis
ordered. Spin-lattice coupling in the disordered Lattice produces an inhomo
geneous magnetic state that allows superconductivity to develop and may con
tribute to observed non-Fermi-liquid effects.