We have investigated the effect of alloying Cu to the Kondo-semimetal CeNiSn on its specific heat, magnetic susceptibility and μSR relaxation rate. We find a strongly non-monotonic behaviour, in that the electronic specific heat first increases very strongly (at 5% Cu), before decreasing again when magnetic order appears (at 10% and 20% Cu). The μSR data show that no spin freezing to a spin glass state occurs for concentrations less than 6% Cu and that the Ce 3 + spins remain in a fluctuating state below this concentration. We interpret this behavior as a consequence of the destruction of the high coherence of the antiferromagnetic spin fluctuations in pure CeNiSn, when Cu is alloyed to the system.