The issue of large intermediate scales is addressed in a class of three-generation models based on the best-known Calabi-Yau compactification of the heterotic string. The renormalisation group equations for this class are studied to determine the scale, μ ≡ M I , at which the first “intermediate-scale” symmetry breaking occurs. Throughout most of the parameter space specifying the models, M I is found to be extremely close to the compactification scale, M c , as is required by phenomenology. This is due to the large number of fields which are massless below M c . Depending on unknown normalisation factors, different directions of symmetry breaking are possible, including the one thus far preferred on phenomenological grounds.