Contours of the minimum eccentricity and inclination dispersions expressed as ﹩{({e}_{\mathrm{rms}}^{2}+{i}_{\mathrm{rms}}^{2})}^{1/2}﹩ to produce a USP planet by secular interactions (Equation (7)) as a function of the mass ratio between the USP planet and the outer planets, and the initial period ratios ﹩{P}_{{\rm{i}}+1}/{P}_{i}﹩ (﹩i=1...{N}_{{\rm{p}}}﹩). The upper panel displays the total number of planets in the system ﹩{N}_{{\rm{p}}}=4﹩, the middle panel N_p = 5, and the lower panel N_p = 6.