The theory of cascade solutions to the Navier-Stokes equations was introduced by Le Jan and Sznitman and later elaborated by Bhattacharya et al. They relied on a pointwise smallness condition of the initial data in the Fourier domain to construct cascade solutions from a branching process. We show how smallness of initial data in some global sense can be sufficient to define cascade solutions. We also show a connection between cascade solutions and mild solutions constructed by fixed point method. Joint work with Enrique Thomann.