It cannot be expected for a Eucalyptus to rocket up to around 16 feet over a period of 3-4 years and then stop growing: it doesn t work like that with Eucalypts, any more than it does for Leyland Cypress, Thuja or Sycamore trees.osition your Eucalyptus at least two thirds its potential mature height away from a building on ordinary loamy garden soils and an even greater distance away from buildings if you have a clay soil (which has a tendency to shrink in periods of drought).