Towering eucalyptus trees, native to Australia and introduced to the rest of the world on a Cook expedition of 1770, thrive in frost-free climates the world over and are particularly popular in California, where in many areas they have replaced native oak woodlands. They provide a great smell from their fruit and welcome shade. Regular pruning is essential because the trees are susceptible to getting blown over when the wind picks up.
Sanitize pruning tools with liquid household bleach diluted with water (ideally, one part bleach for every nine parts water). Submerse tools in solution for a minute or two and then rinse thoroughly (bleach is corrosive to metal). Dry thoroughly with rag.
Trim small branches with pruning shears to thin out the tree and encourage light penetration as well as allow for air and wind movement. Focus on removing branches that cross or rub against other branches. It's better to get rid of problem branches when they are young than when they are big and thick. Branches less than 2 inches thick can almost always be removed with no future problems for the tree.
Avoid cutting off the lower branches of your eucalyptis. Only remove lower branches when they have died on their own. Use a saw and make clean cuts straight through the branch.
Reduce the crown only if necessary, such as situations in which the eucalyptis is top heavy and you live in an area with high winds. Don't remove more than one quarter of a living crown at one time; if more needs to come off, do so over successive years.