Orthodontic brackets (100) formed by machining include tie wings (108) that are pointed at the free end (114) to assist the practitioner in installing ligatures. The bracket (100) includes a bracket body (104) including an arch wire slot (106) formed in the body (104), at least one gingival tie wing, and at least one occlusal tie wing. The free ends (112) of each tie wing (108) extend away from the slot (106). Advantageously, the free end (112) of each tie wing is machined so as to include a compound taper along a distal portion of the tie wing (108). The compound taper creates tapers in the tie wing cross-sectional thickness in both a lingual-buccal dimension (116, 118) as well as in a mesial-distal dimension (120, 122) towards a pointed tip (114) at the distal free end of the tie wing (108). The tapered, pointed free end (114) of the tie wing (108) creates a "purchase point" on which the practitioner can easily hook a standard elastomeric o-ring ligature.