Grassing down around Eucalyptus in later years can help towards restricting and slowing down growth, but should only be done once the tree is happily established and it has grown to at least 3 metres tall.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).