A novel approach to reduce bulk conductance by the use of short period superlattices (SL) of two alternating topological insulator layers is presented. Evidence for a superlattice gap enhancement (SGE) was obtained from the observed reduction of bulk background doping by more than one order of magnitude, from 1.2x10 20 cm -3 to 8.5x10 18 cm -3 as the period of Bi2Se3/Sb2Te3 SLs is decreased from 12 nm to 5 nm, respectively. Tight binding calculations show that in the very thin period regime, a significant SGE can be achieved by the appropriate choice of materials. The ultrathin SL of alternating Bi2Se3 and Sb2Te3 layers behaves as a new designer material with a bulk bandgap as much as 60% larger than the bandgap of the constituent layer with the largest bandgap, while retaining topological surface features. Analysis of the weak antilocalization (WAL) cusp evident in the low temperature magnetoconductance of a very thin period SL sample grown confirms that the top and bottom surfaces of the SL structure behave as Dirac surface states. This approach represents a promising and yet to be explored platform for building truly insulating bulk TIs.