We present Hubble Space Telescope (HST) images of 24 confirmed members of the distant galaxy cluster Cl 0016 + 16 at redshift 0.55. The Balmer-strong (''E + A'') and emission-line galaxies frequently show unusual visual morphology, implying that galaxian interactions produce ''active'' galaxies in moderate-redshift clusters. We use an image concentration index as a quantitative measure of morphology to show that these unusual galaxies appear disklike, while the normal red galaxies resemble E/SO galaxies. Although consistent with HST observations by Dressier et al. in Cl 0939 + 4713 (z = 0.41), our results differ from the Couch et al. finding that most Balmer-strong galaxies in AC 114 (z = 0.31) resemble ellipticals. The entire ''E + A'' sample is small, but if future studies confirm their diversity, it will suggest that they have different origins.