We report a synchrotron x-ray scattering study of the diluted spin-Peierls
(SP) material Cu1-xMgxGeO3. We find that for x > 0 the temperature T-m at w
hich the spin gap is established is significantly higher than the temperatu
re T-m at which the SP dimerization attains long-range order. The latter is
observed only for x < x(c) similar to 0.021, while for x > x(c) the SP cor
relation length quickly decreases with increasing x. We argue that impurity
-induced competing interchain interactions play a decreases with increasing
x. central role in these phenomena.