An Extended Double Zepp has a relatively narrow beamwidth
(~35 deg) and four side lobes about -13 dB down. I vaguely
remember a magazine article that told how to virtually
eliminate the EDZ side lobes.

It was in the vol. 4 Compendium, and it is also in my latest ARRL antenna
book. The technique involves placing about 2500 ohms capacitive reactance on
each leg of EDZ at a strategic location. You can reduce the side lobes, and
provide a better match to 50 ohm coax.
I have been playing around with a 3 element 2 meter EDZ beam that is
currently 17 dbi gain @ 3 deg. elevation with 12 dbi F/B. I used side lobe
reduction on all 3 elements. Be interesting to see if the actual antenna
matches the model.
73 Gary N4AST