Sadly, there is nothing frugal about tree removal. It is costly, and depending on the size of the tree could run you up to $2000 each. As the previous poster stated, it is imperative that whoever you choose is insured. Good luck!
That is good advice about insurance to be sure. I think they usually say they are "bonded". Sometimes you can get a good deal if the trees are large and you let them have the firewood to sell. Sometimes they will give you a deal if they don't have to remove the wood. If that's something you can do yourself you may be able to save.
It really depends on the trees and how many people in your area are providing this service. In fact, some logging companies will actually come remove trees for the lumber if the trees are large. The key is to find someone that knows what they are doing at any price and get some references. I would get a piece of paper and call people in the phone book, and make a list of their services and prices. You should find companies under "Tree" or "Tree Service" in the yellow pages. Call around, make sure they are bonded and like Joe said, call your insurance company too.
I would also go door to door and ask your neighbors if they have had any trees removed and if so, who did it and how much did it cost.
No direct frugal advice I'm afraid - just make sure the company you engage is well insured. I had a large tree cut down and its hair raising to watch them work from the top down. I checked they had proper insurance, and with my insurance company before engaging them in case they fell - and sued! Don't even know if this is a real possibility but it worried me!
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