SWAN, the Solar Wind ANisotropies all-sky hydrogen Lyα camera on the Solar and Heliospheric Observatory spacecraft that makes all-sky images of interplanetary neutral hydrogen, has an ongoing campaign to make special observations of comets, both short- and long-period ones, in addition to the serendipitous observations of comets as part of the all-sky monitoring program. We report here on a study of several short-period comets that were detected by SWAN: 21P/Giacobini-Zinner (1998 and 2005 apparitions), 19P/Borrelly (2001 apparition), 81P/Wild 2 (1997 apparition), and 103P/Hartley 2 (1997 apparition). SWAN observes comets over long continuous stretches of their visible apparitions and therefore provides excellent temporal coverage of the water production. For some of the observations we are also able to analyze an entire sequence of images over many days to several weeks/months using our time-resolved model and extract daily average water production rates over continuous periods of several days to months. The short-term (outburst) and long-term behavior can be correlated with other observations. The overall long-term variation is examined in light of seasonal effects seen in the pre- to post-perihelion differences. For 21P/Giacobini-Zinner and 81P/Wild 2 the activity variations over each apparition were more continuously monitored but nonetheless consistent with previous observations. For 19P/Borrelly we found a very steep variation of water production rates, again consistent with some previous observations, and a variation over six months around perihelion that was reasonably consistent with the spin-axis model of Schleicher et al. and the illumination of the main active areas. During the 1997–1998 apparition of 103P/Hartley 2, the target comet of the EPOXI mission (the Deep Impact extended mission), we found a variation with heliocentric distance (∼r −3.6 ) that was almost as steep as 19P/Borrelly and, given the small measured radius near aphelion, this places a number of possible constraints on the size, shape, and/or distribution active of areas on the surface.