A tray (1) pivotably mounted in an automatic ice maker has a plurality of compartments (4) arranged in a number of rows and separated from one another by partition walls. The wall (6) extending above the upper edges of the partition walls (3) is formed at a longitudinal side of each row of compartments (4) and at at least a part of the transverse sides (2) thereof.For ice making, water (10) is filled into the tray (1) and allowed to freeze therein. Prior to letting the freezing take place, the tray (1) is pivoted from a tilted setting, in which the filled water (10) floods over the partition walls (3) between the compartments (4) of the tray (1) on a part of the width thereof and contacts a region of the longitudinal wall (6) extending above the upper edges of the partition walls (3), to an upright setting, in which the level of the water (10) lies below the upper edges of the partition walls (3).