This work is a study of 5-amino-3-nitro-1,2,4-triazole (ANTA), 3-nitro-1,2,4-triazol-5-one (NTO), and nitrated derivatives of ANTA and NTO. RDX and TNT were studied for comparison. ANTA and NTO are low-sensitive high explosives with detonation properties comparable to 2,4,6-trinitrotoluene (TNT) and 1,3,5-trinitroperhydro-1,3,5-triazine (RDX). We showed previously that nitrated NTO and ANTA compounds, when used in a glycidyl azide polymer (GAP) matrix in rocket propellants, could give impulses above 2600 m/s and that the oxygen balance is positive. If used in aluminized explosives, the heat of detonation may be increased to a practical level significantly above RDX/aluminum compositions. Here, we use two different methods for sensitivity and two density functional theory functionals, B3LYP and M06-2X with the 6-31G(d) basis set, together with the complete basis set method CBS-4M. Calculations indicate that most of the nitrated derivatives have nearly equal sensitivity to RDX. Significantly different bond dissociation energies in the nitrimino functional group are predicted, although most models give much the same result.