A pipe-clamping mattress has a first pipe-clamping block and a second pipe-clamping block. The first and second pipe-clamping blocks have a recessed surface, which together form a cavity for receiving a subsea pipeline. A bottom surface adjacent the recessed surface of each of the first and second blocks is adapted to rest on a seafloor when the recessed surfaces of the first and second blocks are placed around the subsea pipeline.