This paper addresses the principal problem of consciousness, which is to reconcile our experience of subjective awareness with the scientific world view; it is essentially the same as Chalmer's ``Hard Problem.'' This problem arises because subjective experience has a special epistemological status, since it is the personal (and private) substratum of all observation, whereas empirical science is typically based on common (nonpersonal, public) particular observations. Nevertheless, although subjective experience cannot be reduced to physical observables, we may have parallel phenomenological and physical reductions, which inform each other. However, naive introspection is treacherous since it may be unduly influenced by theoretical preconceptions, but phenomenological training aids unbiased (or less biased) analysis of the structure of consciousness. Through phenomenologically trained observers we may acquire unbiased (public) data about the structure of consciousness. (We use ``phenomenology'' and related terms in the sense of Husserl and Heidegger, that is, to refer to the analysis of the phenomena, the given (data) of conscious experience.)