Assuming that Alice commits to an embedding method and the Warden to a detector, we study how much information Alice can communicate at a constant level of statistical detectability over potentially infinitely many uses of the stego channel. When Alice is allowed to allocate her payload across multiple cover objects, we find that certain payload allocation strategies that are informed by a steganography detector exhibit super-square root secure payload (scaling exponent 0.85) for at least tens of thousands of uses of the stego channel. We analyze our experiments with a source model of soft outputs of the detector across images and show how the model determines the scaling of the secure payload.