Cocklebur germinates from deeper in the soil than many weeds.
And it can wait until rains in the mid summer to germinate.
Notill is considered helpful because it leaves the seeds near the surface where they will germinate sooner.
Spray as late as possible with either Roundup or Enlist.
Adding, Roundup in with the Fungicide in July, is probably going to be the best.
Enlist, in with the fungicide, is probably similar.
It just takes a little whiff of roundup to kill cocklebur.
Last year, an August roundup application, easily took out the 6” tall cockleburs down under the canopy as well as the 4’ tall cocklebur above the canopy.
Depending on the rainfall patterns, a late June application could have similar results.