An extended range, consistent force rail brake comprising an adjustable wedge assembly operatively situated between the main power spring(s) and the brake shoe(s) for selectively taking up the vertical distance that the brake shoe is required to travel between the brake release position and an initial railhead contact position. The adjustable wedge assembly is thus selectively expandable in the vertical orientation, and may comprise: an upper block that is operatively connected, either directly or indirectly, to the power spring; a lower wedge rigidly affixed to a replaceable brake shoe; and an intermediate wedge that is located by suitable bearings and/or linkages for transverse, generally horizontal slidable engagement between the upper block and the lower wedge. Each of the upper block and lower wedge elements of the wedge assembly are, respectively, located by suitable bearings and/or linkages for generally vertical translational motion (but very little, if any, lateral or longitudinal horizontal motion) within upper and lower guides provided on a frame of the rail brake.