A bale tie-off accelerator chamber receives bales from the compression chamber of a baler, keeps them compressed and ties them while a new bale is being compressed. The time required to make a bale using the prior art includes the time it takes to push the material into the pressure chamber and then stepwise apply ties to the bale as it is ejected. The present invention allows the complete freshly-compacted bale to be ejected from the pressure chamber before ties are applied, thus allowing the next bale to be formed without waiting for stepwise tying of the preceding bale.