Process for preparing an aluminum oxide powder which is present in the form of aggregated primary particles and comprises at least 85% by weight of alpha-aluminum oxide, in which an aluminum oxide powder which a) is present in the form of aggregated primary particles, b) is selected from the group consisting of gamma-aluminum oxide, theta-aluminum oxide, delta-aluminum oxide and/or X-ray amorphous aluminum oxide, and c) has a tamped density of at least 250 g/l, is subject to a heat treatment at 13000 C or more and subsequently milled. Aluminum oxide powder which can be obtained by this process. Aluminum oxide powder in the form of aggregated primary particles having a BET surface area of from 3 to 30 m2/g, in which the proportion of alpha-aluminum oxide is at least 85% by weight and the ratio dgo/dio of the weight distribution of the primary particles is at least 2.8. Use as constituent of fluorescent tubes.