Analyses of Irish phonological phrasing (Elfner 2012 et seq.) have been influential in shaping Match Theory (Selkirk 2011), an OT approach to mapping syntactic to prosodic structure. We solve two constraint ranking paradoxes concerning the relative ranking of Match and StrongStart. Irish data indicate that while XPs with silent heads can fail to map to phonological phrases in certain circumstances, overtly headed XPs cannot. They also indicate that rebracketing due to the constraint StrongStart occurs only sentence-initially, contrary to predictions. We account for these puzzles by invoking Van Handel's (2019) Match constraint which sees only XPs with overt heads, and by positing a new version of StrongStart which only applies to material at the left edge of the intonational phrase. Our analysis is developed using the Syntax-Prosody in Optimality Theory application (SPOT) and OTWorkplace.