  The perfect space-time block codes (STBCs) are based on four design criteria
- full-rateness, non-vanishing determinant, cubic shaping and uniform average
transmitted energy per antenna per time slot. Cubic shaping and transmission at
uniform average energy per antenna per time slot are important from the
perspective of energy efficiency of STBCs. The shaping criterion demands that
the {\it generator matrix} of the lattice from which each layer of the perfect
STBC is carved be unitary. In this paper, it is shown that unitariness is not a
necessary requirement for energy efficiency in the context of space-time coding
with finite input constellations, and an alternative criterion is provided that
enables one to obtain full-rate (rate of $n_t$ complex symbols per channel use
for an $n_t$ transmit antenna system) STBCs with larger {\it normalized minimum
determinants} than the perfect STBCs. Further, two such STBCs, one each for 4
and 6 transmit antennas, are presented and they are shown to have larger
normalized minimum determinants than the comparable perfect STBCs which
hitherto had the best known normalized minimum determinants.
