A new approach is suggested to the theory of ramification in finite extensions of complete discrete valuation fields in the case of an imperfect residue field. It is based on the notion of a distance between extensions that shows the difference in ramification depths arising after a base change of a certain type. For two-dimensional local fields of prime characteristic, the following is proved. If the distance between two constant extensions (i.e., extensions defined over a given field with perfect residue field) is zero, then the corresponding Hasse-Herbrand functions coincide. The converse is verified only for extensions of degree p.