Cooperative scattering of light by an extended object such as an atomic ensemble or a dielectric sphere is fundamentally different from scattering from many pointlike scatterers such as single atoms. Homogeneous distributions tend to scatter cooperatively, whereas fluctuations of the density distribution increase the disorder and suppress cooperativity. In an atomic cloud, the amount of disorder can be tuned via the optical thickness, and its role can be studied via the radiation force exerted by the light on the atomic cloud. Monitoring cold (87)Rb atoms released from a magneto-optical trap, we present the first experimental signatures of radiation force reduction due to cooperative scattering. The results are in agreement with an analytical expression interpolating between the disorder and the cooperativity-dominated regimes.