Sara, while some pics would help, it doesn't sound to me as though any pruning needs to be done. A little tip browning is normal for all arbs and will be completely obscured by new growth later. Also, GGs have a strongly predetermined growth form. Any pruning done in this regard will, IMO, make them worse, not better. Now if there was to be a whole complete branch that died for some reason, that should be removed. but it doesn't sound to me like this is the case.

As to fertilizing, if the trees are surrounded by turf that is receiving regular fertilization, the trees will be getting enough from that. Even where this is not the case, folks tend to want to overuse fertilizer on trees. Mostly, they don't need it. But.......a moderate dosing of some nitrogen could well speed up top growth on the plants. Just go very mellow with it, if at all.

The GG grows so fast that there tends to be some space between branches where the stem has elongated. Please resist the tempatation to "fix" this. They will be just fine, filling in as side branchlets elongate and multiply over time. To me and many others, the best possible appearance with most conifers is achieved when we do nothing to alter it. Be patient and I think you will see this too.

+oM

Generally, I agree with what Tom said, but I will make two points.

One is that if your trees seem to be producing codominant leaders, I would strongly suggest pruning to eliminate this situation. Single leader trees will hold up much better with snow or ice loading. Thujas take pruning very well, so if you do need to prune them, it shouldn't be a problem.

The second point is that trees really shouldn't be fertilized unless they need it. A soil test is about the only way to be sure if some nutrient is missing. Fertilizing trees can, in some cases, actually be detrimental to tree's health. This has been covered many times in this forum, so if you wanted to know more about it, I'm sure a search would turn up many posts.

GG's, to the best of my knowledge, are single stemmers. I guess without pics we can only guess as to what the OP's "floppy branches" actually consist of. My feeling is that with many areas of the country having had heavy Winter precipitation, many folks are getting bent out of shape (There, I said it again;^) about things not being in perfect alignment, when in fact, time will take care of these issues all by itself.

One of the conundrums about the fertilizer debate is that almost without exception, the addition of nitrogen to the soil a plant is growing in WILL elicite a response-increased top growth, and that is one definition of when a fertilizer is "needed", when its' addition will provoke a positive growth response. But, but, but, there's more to it, and stimulating too much top growth relative to the plants root system can put it in jeaopardy in a number of ways, so if you do any fertilizing, the best bet is to go very low with the amount.

+oM

The ones I have seen with double leaders were not.

I think a good way to sum it up is to say that, except maybe for extreme drought like we had in my area of the country last year, Green Giants are really good about taking care of themselves with minimal intervention by the gardener.

Just like the parent species it derives from, 'Green Giant' will develop a forked trunk if it loses its top, or has its top cut out. They're not invariably single-stemmed.

Resin