Demure

a. [From O. Fr. de murs, i. e., de bonnes murs, of [good] manners; O. Fr. murs, mours, meurs, mors, now mœurs, f., Pr. mors, sing. mor, f., from Lat. mores, sing. mos, manners, morals.]

1. Of sober or serious mien; composed and decorous in bearing; of modest look; grave. “With countenance demure, and modest grace.” Spenser.
2. Hiding immodesty, vivacity, or interested attention, under a decorous, or serious, or careless demeanor; modest in outward seeming only; making a show of gravity.

A cat lay, and looked so demure, as if there had been neither life nor soul in her. L’Estrange.