A firearm sighting system includes a rear sight unit having a plurality of separate sight elements adaptable for "zeroing" the same gun with different ammunition. In preferred embodiments, a rear sight unit comprises windage and elevation adjustments for each of two sight elements, 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 elevation-adjustable front sight unit, which may act as an extension member for 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. Alternatively, the rear sight unit multiple sight elements may comprise only one that is windage adjustable and elevation adjustable, which rear sight unit may cooperate with a front sight unit that has one sight element that is windage adjustable and elevation adjustable.