A heddle shaft (1) with heddles (3) that are supported with little play or free of play has at least one heddle support rail (7), which is supported movably for elastically tensing the heddles (3) as a whole, or has at least one movably supported part (55). A spring means (16, 56) serves to exert a tensing force on the heddle head (5) of each heddle (3) for supporting that heddle without play. This makes a high operating speed of a power loom, provided with such a heddle shaft, possible without the heddles digging into the heddle support rails and without producing excessive noise.