In this paper, I examine the prosodic nature of unstressed function words in Spanish. I defend the hypothesis that these words, like all other words in the language, have a syllable that is lexically designated as stressed. I suggest that the essential property of these words is that they are subject to a rule of prosodic merger with following elements within the syntactic phrase, creating a single prosodic word domain. Their surface stresslessness, I argue, is a consequence of the fact that, by a general rule operating in the language, only the rightmost lexical stress is preserved within a prosodic word domain in Spanish. I also consider several pragmatic contexts in which these words may receive stress in discourse. Finally, I briefly compare stresslessness in Spanish with accentlessness in Basque and tonelessness in Bantu languages. (Contains 8 figures.)