  Heisenberg-type spin-chain materials have been extensively studied over the
years, yet not much is known about their behavior in the presence of disorder.
Starting from BaCu$_2$Si$_2$O$_7$, a typical spin-1/2 chain system, we
investigate a series of compounds with different degrees of bond disorder,
where the systematic replacement of Si with Ge results in a re-modulation of
the Cu$^{2+}$ exchange interactions. By combining magnetometry measurements
with nuclear magnetic resonance studies we follow the evolution of the
disorder-related properties from the well-ordered BaCu$_2$Si$_2$O$_7$ to the
maximally disordered BaCu$_2$SiGeO$_7$. Our data indicate that already a weak
degree of disorder of only 5% Ge, apart from reducing the 3D magnetic ordering
temperature $T_\mathrm{N}$ quite effectively, induces a qualitatively different
state in the paramagnetic regime. At maximum disorder our data indicate that
this state may be identified with the theoretically predicted random singlet
(RS) state. With decreasing disorder the extension of the RS regime at
temperatures above $T_\mathrm{N}$ is reduced, yet its influence is clearly
manifest, particularly in the features of NMR relaxation data.
