A solution to the diffusion controlled growth of needle and plate shaped particles is presented as their shape approaches respectively a paraboloid of revolution or a parabolic cylinder, under small supersaturation values, when capillarity and interface kinetic effects are present. The solutions show that as supersaturation decreases, the growth rate and needle tip radius approach a common value regardless of interfacial kinetics effects as capillarity is the main factor that retards particle growth. Simple asymptotic expressions are thus obtained to predict the growth rate and tip radius at low supersaturations, assuming a maximum velocity hypothesis. These represent the circumstances during solid state precipitation reactions which lead to secondary hardening in steels.