A sound attenuating cover is adapted for intimate fitment to a compressor of a domestic air conditioner, and comprises an outer sleeve member and a generally circular top member which is releasably secured to the outer sleeve member. Hook and loop fasteners secure a first end of the outer sleeve member to a portion of the outer periphery of the sleeve member. When the closure member secures the top member to the outer sleeve member, and the hook and loop fasteners are secured, a cylindrical cover having a closed top end is formed having a diameter adapted for intimate fitment to a compressor of a domestic air conditioner. Each of the outer sleeve member and the circular top member comprises inner and outer cover sheeting material, and at least one layer of sound attenuating material which is typically glass fiber together with barium loaded vinyl.