In 2017 Chemin, Zhang and Zhang posed the question of whether initial data with small third-component (with respect to a scale-invariant norm) implies global regularity of the associated 3D Navier-Stokes solution. Motivated by this open question, in this talk I will discuss growth properties of solutions for certain initial data with zero third-component. This talk is based on joint work with Christophe Prange (Cergy) and Jin Tan (Chinese University of Hong Kong).