Several II–IV double-ReO3-type (DROT) fluorides are known to exhibit strong negative thermal expansion (NTE) over a wide temperature range while retaining a cubic structure down to 120 K or lower. CaZrF6, CaNbF6, CaTiF6, and MgZrF6, embody these properties. In contrast to the behavior of these II–IV materials, the I–V DROT material, NaSbF6, has been reported to display a phase transition from rhombohedral to cubic above 300 K and positive thermal expansion both above and below the transition. In this work, NaNbF6 and NaTaF6 are shown to undergo first-order cubic-to-rhombohedral transitions on cooling to ∼130 K. Above this transition, NaNbF6 shows modest NTE between 160 and 250 K, whereas NaTaF6 exhibits near-zero thermal expansion over the range 210–270 K. These I–V systems are elastically softer than their II–IV counterparts, with a zero pressure bulk modulus, K0, of 14.6(8) GPa and first derivative of the bulk modulus with respect to pressure, K0′, of −18(3) for cubic NaNbF6, and K0 = 14.47(3) GPa and K0′= −21.56(7) for cubic NaTaF6. When subject to ∼0.3 GPa at 300 K, both compounds exhibit a phase transition from Fm3̅m to R3̅. The R3̅ phases exhibit negative linear compressibility over a limited pressure range. A further transition with phase coexistence occurs at ∼2.5–3.0 GPa for NaNbF6 and ∼4.5 GPa for NaTaF6. Compression of NaNbF6 in helium at room temperature and below provides no evidence for helium penetration into the structure to form a perovskite with helium on the A-site, as was previously reported for CaZrF6.