We report on the sensitivity of SPIRE photometers on the Herschel Space Observatory. Specifically, we measure the confusion noise from observations taken during the science demonstration phase of the Herschel Multi-tiered Extragalactic Survey. Confusion noise is defined to be the spatial variation of the sky intensity in the limit of infinite integration time, and is found to be consistent among the different fields in our survey at the level of 5.8, 6.3 and 6.8 mJy/beam at 250, 350 and 500 μ...