To me it appears that the suckers grow more tomatoes, so if that's the case why trim them off? It looks like the thing below the sucker--the "leaf branch"?--is what needs to be trimmed off. So far most of the time I take people's advice and trim the suckers, but when the suckers have blossums or are a lot bigger than the leaf branch I leave the suckers and trim the branch. From my pov the branch seems like the sucker and the sucker seems like what we would want to keep. The sucker always seems to grow nice and strong, while the leaf branch seems to be sort of shriveled with poor leaves. Do those branches even grow tomatoes at all? Looking at mine I see several succers with blossums, I haven't noticed any on the other branches.