A bracket system comprising: a bracket combinatorial library including a plurality of brackets each interchangeably fixedly mountable to each of a plurality of teeth within a dentition group in a dental arch, each of said plurality of brackets within said bracket combinatorial library including: a bracket base having one configuration fixedly mountable to each one of said plurality of teeth within said dentition group; said bracket base having a bracket base mounting surface adapted for directly bonding to the surfaces of respective said teeth; a bracket body having a bracket body length disposed between a bracket body first end and a bracket body second end, said bracket body first end coupled to said bracket base, said bracket body second end extending outwardly from said bracket base and an archwire slot extending across said bracket body second end, said archwire slot defined by an archwire slot base joined to a pair of archwire slot walls disposed a distance apart in substantially parallel opposed relation, said archwire slot having an archwire slot angle relative to said bracket base, said archwire slot configured to receive an archwire; wherein said plurality of brackets within said bracket combinatorial library includes a plurality of preselected bracket body lengths discretely occurring throughout a bracket body length range of between zero millimeters to about 5 millimeters; wherein said plurality of brackets within said bracket combinatorial library includes a plurality of preselected archwire slot angles discretely occurring throughout an archwire slot angle range of between 0 degrees to about 60 degrees; wherein each one of said plurality of preselected bracket body lengths discretely combines with each one of said plurality of preselected archwire slot angles; and whereby the number of said plurality of brackets within said bracket combinatorial library associated with said dentition group being equal to the product of the number of different preselected bracket body lengths occurring throughout said bracket body length range times the number of different preselected archwire slot angles occurring throughout said archwire slot angle range characterized in that said bracket base having a bracket base mounting surface with a concave or convex contour configured to conform to a corresponding convex or concave contour of a mountable tooth surface. a bracket combinatorial library including a plurality of brackets each interchangeably fixedly mountable to each of a plurality of teeth within a dentition group in a dental arch, each of said plurality of brackets within said bracket combinatorial library including: a bracket base having one configuration fixedly mountable to each one of said plurality of teeth within said dentition group; said bracket base having a bracket base mounting surface adapted for directly bonding to the surfaces of respective said teeth; a bracket body having a bracket body length disposed between a bracket body first end and a bracket body second end, said bracket body first end coupled to said bracket base, said bracket body second end extending outwardly from said bracket base and an archwire slot extending across said bracket body second end, said archwire slot defined by an archwire slot base joined to a pair of archwire slot walls disposed a distance apart in substantially parallel opposed relation, said archwire slot having an archwire slot angle relative to said bracket base, said archwire slot configured to receive an archwire; a bracket base having one configuration fixedly mountable to each one of said plurality of teeth within said dentition group; said bracket base having a bracket base mounting surface adapted for directly bonding to the surfaces of respective said teeth; a bracket body having a bracket body length disposed between a bracket body first end and a bracket body second end, said bracket body first end coupled to said bracket base, said bracket body second end extending outwardly from said bracket base and an archwire slot extending across said bracket body second end, said archwire slot defined by an archwire slot base joined to a pair of archwire slot walls disposed a distance apart in substantially parallel opposed relation, said archwire slot having an archwire slot angle relative to said bracket base, said archwire slot configured to receive an archwire; wherein said plurality of brackets within said bracket combinatorial library includes a plurality of preselected bracket body lengths discretely occurring throughout a bracket body length range of between zero millimeters to about 5 millimeters; wherein said plurality of brackets within said bracket combinatorial library includes a plurality of preselected archwire slot angles discretely occurring throughout an archwire slot angle range of between 0 degrees to about 60 degrees; wherein each one of said plurality of preselected bracket body lengths discretely combines with each one of said plurality of preselected archwire slot angles; and whereby the number of said plurality of brackets within said bracket combinatorial library associated with said dentition group being equal to the product of the number of different preselected bracket body lengths occurring throughout said bracket body length range times the number of different preselected archwire slot angles occurring throughout said archwire slot angle range characterized in that said bracket base having a bracket base mounting surface with a concave or convex contour configured to conform to a corresponding convex or concave contour of a mountable tooth surface.