This contribution examines various aspects of "openness" in research, and seeks to gauge the degree to which contemporary "e-science" practices are congruent with "open science." Norms and practices of openness are held to have been vital for the work of modern scientific communities, but concerns about the growth of stronger technical and institutional restraints on access to research tools, data and information recently have attracted notice - in part because of their implications for the effective utilization of advanced digital infrastructures and information technologies in research collaborations. Our discussion clarifies the conceptual differences between e-science and open science, and reports findings from a preliminary look at practices in U.K. e-science projects. Both parts serve to underscore the point that it is unwarranted to presume that the development of e-science necessarily promotes global open science collaboration. As there is evident need for further empirical research to establish where, when, and to what extent "openness" and "e-ness" in scientific and engineering research may be expected to advance hand-in-hand, we outline a framework within which such a program of studies might be undertaken.