To obtain a satisfactory performance with a star-star transformer it is sometimes, but not always, necessary to provide the transformer with a delta-connected tertiary winding. Much misapprehension exists among electrical engineers about the reasons for such a winding, and most users of these transformers in Britain demand a delta winding in all instances, although, in fact, its additional cost is often not justified and its provision is technically undesirable. The subject is rarely mentioned in textbooks and then, as a rule, only briefly. The authors of this article explain in plain words when a star-star transformer should be fitted with the extra winding. This will be familiar to transformer specialists, but it is believed that the article will be useful to many other electrical engineers who use star-star transformers and enable them to decide whether a tertiary winding is necessary in a particular transformer. The authors show that in most instances a decision can be reached easily and without an exact numerical assessment.