Apparatus for noise reduction in valves are disclosed herein. An example valve disclosed herein includes a valve body defining a fluid passageway between an inlet and an outlet, a plug, and a cage in the fluid passageway. The plug is disposed in the cage. The plug is moveable in the cage to control fluid flow through the fluid passageway. The cage includes an inner wall having first openings, an outer wall having second openings, the outer wall disposed coaxially around the inner wall, and an insert having third openings. The insert is disposed between the inner wall and the outer wall.