Yup, when you add a full wave rectifier, you get a little more output.
In the end, though, its the cap across the DC output that reduces the flicker.
The non ghosting led's add another cap inside the case, more caps, less flicker.
Thats why power supplies have primary caps before the regulator, secondary caps after the regulator, and usually the ceramic glitch eaters at the chip power lead. all in an effort to smooth out that flicker we all love so much.