The present invention relates to a glassmaking furnace regenerator comprising a stack, between a first face and a second face, of several rows of refractory members, the refractory members of each row defining a plurality of channels, in which regenerator a region of the stack that extends from the first face to a height less than 50% of the total height of the stack, known as the first region (22), comprises at least one transverse section (121, 122; 12'1, 12'3), known as a narrow channel section, in which at least 75% of the channels have, in any transverse sectional plane, an opening having a width (l) of less than 0.16 m, the combined height (Ht) of all of said narrow channel sections in the first region being greater than 0.5 m.
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