Each end of the antenna was tied to trees with a rope. There was no give, so if one of the trees swayed enough in the wind, the antenna might break apart.
In the past, I used weighted plastic bottles as counterweights. But I thought there might be a better and simpler way, so I searched the Internet for ideas.
Somebody suggested bungee cords. (Why hadn't I thought of that?) So I bought some new bungee cords, shortened the rope on each end of the antenna, and placed a bungee cord between eye hooks bored into each tree and the shortened ropes.
Worked like a charm!