I grow eucalyptus and have the problem you describe if I harvest it in the summer. However, if I wait about another 6 weeks until sometime in October then it is just fine. I don't know if it is the onset of cooler weather or the plants being more mature. I now only use it for my fall bouquets.
Kirk

Dear Kirk,

thanks - I'll wait a bit longer and see how it goes in September/October. Perhaps they're simply too soft now.

I planted mine from seed two years ago. When I cut them I put them in plain water and sit overnight to make sure they don't wilt. Some times you can cut off the tips of the leaves that haven't quite hardened off. They seem to do just fine, cut in the morning.
Kathy