A sighting system for a firearm includes a rear sight unit having a plurality of separate sight elements adaptable for "zeroing" the same gun with different ammunition. The multiple-zero sight unit comprises windage and elevation adjustments for each sight element, so that multiple ammunition types having different trajectories may be fired accurately from a single firearm after zeroing-in one of the plurality of sight elements for each of the different ammunition types. Preferably, the separate sight elements may be connected to each other or to a common pivot arm or movable bracket so that moving one sight element into the sight path automatically removes the other from the line of vision. Elevation adjustments may be done in various ways, for example, by sliding sight elements out along an arm or bracket, or by changing an angle of the arm or bracket relative to the firearm. The preferred sighting system also includes an adjustable front sight unit, which can be raised or lowered in elevation, by sliding a fin or blade up or down or by adding or removing an extension member. Adding the extension member may provide a gross adjustment of the front end of the firearm by significantly lowering the barrel position for a given line of sight between the user's eye, the selected rear sight, and the front sight.