A fabric (30) includes a first flexible fabric layer (32), having fabric emissivity properties in a visible radiation range that are selected so as to mimic ambient emissivity properties of a deployment environment of the fabric, and at least one second flexible fabric layer (34), which is joined to the first flexible fabric layer, and which is configured to scatter long-wave radiation that is incident on the fabric. The first and second flexible fabric layers are perforated by a non-uniform pattern of perforations (44) extending over at least a part of the fabric.