The headword here, a compound adjective, is found twice in extant classical literature: Homer and Theocritus.
(i) In Homer, Iliad 5.707, it refers to the waistband of the Boeotian Oresbius (mentioned only at the time of his death). Its first element should refer to the movement of the wearer, as Leaf points out in his edition of the Iliad ad loc. (cf. p.188), not to the mi/trh (although it is seldom translated that way). The definition comprises the first three words of that in the ancient Etymologica, poiki/lhn mi/tran e)/xonta, e)c ou(= eu)ki/nhton, polemisth/n ('a warrior with a multicoloured or intricately crafted mitre, because of which he moved easily', Etymologicum Genuinum alpha221, Etymologicum Magnum 37.21, Etymologicum Symeonis 1.156.27). As with all uses of ai)o/los (alphaiota 253) and its compounds, it is impossible to decide among the possible meanings (if it applies to the mitre).
In Homer mi/trh refers to an uncertain part of the warrior's protection for the waist or upper body, almost certainly also serving as a loincloth or attached to it (see de Leeuw in bibliography below). It is most likely to be the well-documented waistband of Mycenaean armour (see Brandenburg in bibliography). Like a shield or greaves the latter might be made of leather coated with bronze. It sharply constricted the waist of a warrior, and thereby probably protected him at the narrow part of the figure-of-eight shield (Buchholz/Wiesner, fig.2, p.8, with a clear illustration of the mitre as girdle) and increased his upper-body agility in shield and spear fighting. We may, with some confidence, take this as the meaning of the headword in Homer.
(ii) After Homer the word mi/tra, mi/trh may still be used of the baldric that carries a quiver (Apollonius Rhodius, Argonautica 3.156), or of a virgin's girdle (Gow 491, note 55) or a wrestler's (Greek Anthology 15.44), passing between the legs. But elsewhere it is used almost exclusively for a headdress, with oriental associations, usually a cincture (bandana, chaplet, crown, exactly as modern mitre) or diadem, the sense in which our headword is found at Theocritus, Idylls 17.19. Gow, in his superb note on this passage (see bibliography), points out that ai)olo- here probably means 'multicoloured', citing Athenaeus, Deipnosophists 12.536A (12.50 Kaibel) (= D(o)uris of Samos [OCD(4) p.480] fr. 31 Mette, FGrH 76 F14), on the mitre of Demetrius Poliorcetes, and Curtius Rufus (OCD(4) p.400) 6.6.4, on Alexander's.