vivaldi antenna pattern

what parameters of the geometry of a Vivaldi antenna affect its directivity?
I have an array and want to make the 3dB bandwith narrower. Apart from doing some tappering I'd like to change the radiating elements for another more directive Vivaldis and try to pull down the NLS that increases when tappering. The tappering I'd use to make the bandwith narrower, is an inverted triangular feed, which would also narrow the whole diagram and increase the NLS.

So, how directive can a Vivaldi be?

Added after 19 minutes:

taking into account that the array is broadside, it is not a scanning array. I think it should be an array of more directive elements, not Vivaldis.
Vivaldis are good for scanning arrays, but for a broadside, shouldn't it be better a more directive element such as a V dipole?

thanks