I have several trees in my yard, and it's a nice size yard, but the trees are in the wrong places for the antennas I wanted. I wanted to use a simple dipole with it's lobes radiating east and west for best coverage (I live 20 miles west of Chicago). Let the compromises begin...
If I put up a vertical support (a 1-1/2" x 10' length of PVC pipe in a tripod) in the middle of my roof, I could manage an inverted vee which is close to the dipole I really wanted. The problem then was my roof wasn't big enough for a full-size 30m inverted vee with a 90 degree angle at the vertex. So I would have to add some loading to shorten the legs of the vee.
An article, "Designing a Shortened Antenna", by Luis Lopes in the October 2003 QST, pages 28-32 got me started in the right direction. I bought a new Antenna Handbook just in case the physics for dipoles had changed since 1976, so I'll reference the information in the newer handbook just to be current. The table on page 6-31 says that you can achieve a half-size antenna by putting 1000 ohm inductors in the middle of each leg of the vee. And the QST article says that the more wire you can have between the center insulator and the inductor, the more efficient the antenna will be. So I wound the coils and put them in the midpoint of each leg of the vee. I put the other half of the wire on the "far" side of the coils and checked to see if I could tie them to the edge of the roof with a few feet of rope. The result was that I actually had a few extra feet of roof left over. So it was time to lengthen the "inner" wire lengths until I was making optimum use of the space I had. Now it was time to remove some turns on the coils since I'm no longer shortening the antenna by 50%. In about an hour, I had the new coils defined. I should mention that I also bought an MFJ-259B Antenna Analyzer. That instrument gives me the confidence that the change I made was doing what I expected.
This antenna worked so well, I repeated the process to make a 40m inverted vee using a PVC pipe mounted to my tower and sticking out 4 feet for the vertex support. This one also fits on the roof.