We give a simple proof of the known S-duality of heterotic String theory compactified on a ⁶. Using this S-duality we calculate the tensions for a class of BPS 5-branes in Heterotic String theory on a S¹. One of these, the Kaluza-Klein monopole, becomes tensionless when the radius of the S¹ is equal to the string length. We study the question of stability of the heterotic NS5-brane with a transverse circle. For large radii the NS5-brane is absolutely stable. However for small radii it is only marginally stable. We also study the moduli space of 2 Kaluza-Klein monopoles and show that it is equal to the moduli space of a heterotic A₁ singularity.