This paper proposes a model of stress assignment in which metrical structure is built serially -- one foot at a time -- through a series of OT-style evaluations.  Iterative foot optimization (IFO) is made possible in the framework of Harmonic Serialism, which defines the path from an input to an output with a series of gradual changes in which each form is more harmonic than its predecessor, relative to a constraint ranking.  Stress assignment in IFO is compared to parallel OT and it is found that they predict different classes of languages even when the same standard stress constraints are considered.  IFO makes the strong prediction that decisions about metrical structure are made locally, while parallel OT predicts stress systems with non-local interactions.  The interactions of stress with syllable weight, vowel shortening, and edge restrictions are considered, and in all cases it is shown that attested languages exhibit local interactions, while parallel OT predicts non-local counterparts which are not clearly attested.