Buoyancy modules for subsea riser pipes are made of syntactic foam solid cores covered with tough high density polyethylene shells. Inner surfaces have partial semi-cylindrical surfaces to fit the riser pipes. Internal radial grooves hold flexible contact pads. Recesses in the inner surfaces hold auxiliary lines. Flat surfaces between the inner and outer semi-cylindrical surfaces have complementary longitudinally extending semi-cylindrical grooves to position choke and kill lines. Grooves in the outer semi-cylindrical surfaces hold composite fiber tensioning straps directly outward from the flexible contact pads. Flat areas of the grooves hold tensioning hardware. Tensioning the straps grips the riser pipe with the pads and grips the choke and kill lines in the semi-circular grooves. Cavities in the ends allow the buoyancy module halves to be assembled on the riser pipe around clamps which hold the accompanying lines.