High voltage semiconductor devices with high-voltage termination structures are constructed on lightly doped substrates. Lightly doped p-type substrates are particularly prone to depletion and inversion from positive charges, degrading the ability of associated termination structures to block high voltages. To improve the efficiency and stability of termination structures, second termination regions of the same dopant type as the substrate, more heavily doped than the substrate but more lightly doped than first termination regions, are positioned adjoining the first termination regions. The second termination regions raise the field threshold voltage where the surface is vulnerable and render the termination structure substantially insensitive to positive charges at the surface. The use of higher dopant concentration in the gap region without causing premature avalanche is facilitated by only creating second termination regions for regions lacking field plate protection.