More paracompact box products

This is the published version, also available here: http://dx.doi.org/10.1090/S0002-9939-1979-0521893-2. First published in Proc. Amer. Math. Soc. in 1979, published by the American Mathematical Society.We show that if there is no family of cardinality less than c which dominates ww, then the box product of countably many compact first-countable spaces is paracompact; hence the countable box product of compact metrizable spaces is paracompact if 2w = w2. We also give classes of forcing extensions in which many box products are paracompact