A new rule for modulating costs in side-informed steganography is proposed. The modulation factors of costs are determined by the minimum perturbation of the precover to quantize to the desired stego value. This new rule is contrasted with the established way of weighting costs by the difference between the rounding errors to the cover and stego values. Experiments are used to demonstrate that the new rule improves security in ternary side-informed UNIWARD in JPEG domain. The new rule arises naturally as the correct cost modulation for JPEG side-informed steganography with the “trunc” quantizer used in many portable digital imaging devices.