A continuously flowing glass stream is conditioned and homogenized along a conditioning stretch, which extends from an entry side to at least one extraction point, and at the beginning of which there is a cooling zone, to which at least one homogenizing zone for the glass temperature is connected. In the working end or the distribution channel the temperature is reduced from the entry temperature T1 to an outlet temperature T2. In order to achieve the necessary conditioning and homogenization, even at high throughputs, the glass stream in the at least one cooling zone of the working end or distribution channel has a cross section with a depth/width ratio D/W of a maximum 0.6, or 0.5, or 0.4, or 0.3 or 0.2, whereby the maximum depth Dmax amounts to 300 or 250 or 200 mm, achieved by at least one bank raised from the bottom, and at least 50, or 60, or 70% of that amount of energy which corresponds to the temperature difference between T1 and T2 is removed from the glass bath along the total length of all the cooling zones.