PLEASE NOTE DIFFERENT DATE, TIME AND LOCATION.  We generalize a well-known result due to Escauriaza-Seregin-Sverak by showing that Navier-Stokes solutions cannot develop a singularity if certain scale-invariant spatial Besov norms remain bounded in time. Our main tool is profile decompositions for bounded sequences in Banach spaces, and we follow the general dispersive method of "critical elements" developed by Kenig-Merle. This is joint work with I. Gallagher and F. Planchon, based on previous work with C. Kenig.