It is shown that infinitely many heterotic string theories exist in uncompactified dimensions less than 10, that are one-loop finite (for massless external legs). Tachyons are removed by compactifying into tori (10 - d) and (26 -d) dimensions of the right-moving superstring and left-moving bosonic string sectors, respectively. The condition for modular invariance is shown to be equivalent to self-duality condition on even lorentzian lattices with (10 -d) and (26 -d) timelike and spacelike directions, respectively. The construction results in a (10 -d)(26 -d) parameter family of one-loop finite string theories. The zero mass sector of these theories for d = 4 and 6 correspond to N = 4 and 2 supergravity coupled to super Yang-Mills with many possible groups, some of which cannot be obtained by compactifying d = 10 heterotic string theory.