Save weight, get a Perrin shorty antenna. Seriously, though, the Perrin shorty antennas are an easy way to spruce up the appearance of your BRZ. Perrin offers 2" & 4" replacement antennas for the OEM Subaru unit. The Perrin antennas feature an attractive, anodized black finish that looks great with the OEM base and installs in minutes.
Shorty antennas will not improve your reception. Reception quality usually diminishes with a shorter antenna. Dang do they look good though.