Rubintropfen, Sorry to chime in so late. I know how you feel about having to call the "PROS". This can be done fairly safely several ways as a DIY job. The deuce and a half with a winch is good but although slower even a long chain and a comealong can do the job with this proviso...
You have to have something to anchor the comealong.
Perhaps there are suitable trees close enough to use but far enough away to be safe. Put a chain or cable (rope stretches a lot under load, storing up a lot of energy and can cause you lots of grief if it breaks or something comes lose) around the tree to be removed and run it a safe distance toward your anchor. There are wide straps with attachment points at each end made for this (Warn winch company and others sell them or make your own. They prevent damage to the anchor tree.)
Two comealongs work well.
Attach the comealong to the anchor (use the tree saving strap). Set strap as low to ground as is practical.
The other end of the extended comealong hooks to the chain that runs to the tree to be removed.
Repeat the following steps until the tree is horizontal on the ground where you can cut it up safely.
1. Ratchet in the comealong
2. Extend the other comealong and hook onto the chain (similar to first).
3. Ratchet in this comealong which frees up the other.
4. Extend the free comealong and attach to chain
Is tree in question horizontral on ground yet?
Yes... cut it up
No... repeat the above steps
OK, so much for pseudo code and computer programming... In reality the tree may be tall in comparison to your chain so... You might have to select a second, third, xxx anchor to stay far enough from the tree being removed to remain safe. I assumed poor access to tree to be removed. If it is within a cable distance from where you can get a truck or tractor (maybe after a few applications of the comealong) you could try the vehicle as an anchor. You can pad the bumper of a truck and anchor to the truck letting the tension try to pull the truck through a "helper" tree. Sometimes the vehicle can't do the job at first but can after you do the "heavy lifting" with comealongs.
Comealongs are cheap a real bargain. Get a couple HD units beefier than you think you will ever need and you will probably eventually have occasion to be real glad you didn't save a couple bucks and buy flimsy ones. A few bucks spent there is good insurance.
About calling the pros. Be safe. If it isn't safe, call the pros. Better you call the tree pros than your widow calls the enbalming pros. That said, if you are careful and use really beefy chain and comealongs and select robust anchor points there is no reason you can't pull down a quite substantial "Sword of Damacles".
Patrick