Copolycarbonates comprising as chain terminators the structural unit derived from p-tert-butylphenol and at least one diphenol unit of the formula in which R 3 represents C 1 -C 4 -alkyl, R 4 represents hydrogen or C 1 -C 4 -alkyl, n represents 0, 1, 2 or 3, and at least one dihydroxyaryl compound of the formula HO-Z-OH in which Z represents a radical of the formula in which R 6 and R 7 independently of one another represent H, C 1 -C 18 -alkyl, C 1 -C 18 -alkoxy or halogen or represent aryl or aralkyl, each of which is optionally substituted, and X represents C 1 - to C 6 -alkylene, C 2 - to C 5 -alkylidene or C 6 - to C 12 -arylene; wherein copolycarbonates have the following inhomogeneity factors: A) copolycarbonates having a content of ≥ 50 mol% and < 100 mol% of diphenol unit of the formula, based on the sum of the diphenols: for linear CoPC having an average molecular weight (weight-average) of from 18,000 to 35,000 g/mol, U = (Mw/Mn)-1 is 1.3 to 2.3, B) copolycarbonates having a content of greater than 0 and less than 50 mol% of diphenol unit of the formula, based on the sum of the diphenols: for linear CoPC having an average molecular weight (weight-average) of from 16,000 to 35,000 g/mol, U = (Mw/Mn)-1 is 1.2 to 2.4; and wherein the copolycarbonates have been prepared by a continuous phase interfacial process. R 3 represents C 1 -C 4 -alkyl, R 4 represents hydrogen or C 1 -C 4 -alkyl, n represents 0, 1, 2 or 3, and at least one dihydroxyaryl compound of the formula HO-Z-OH in which Z represents a radical of the formula in which R 6 and R 7 independently of one another represent H, C 1 -C 18 -alkyl, C 1 -C 18 -alkoxy or halogen or represent aryl or aralkyl, each of which is optionally substituted, and X represents C 1 - to C 6 -alkylene, C 2 - to C 5 -alkylidene or C 6 - to C 12 -arylene; wherein copolycarbonates have the following inhomogeneity factors: A) copolycarbonates having a content of ≥ 50 mol% and < 100 mol% of diphenol unit of the formula, based on the sum of the diphenols: for linear CoPC having an average molecular weight (weight-average) of from 18,000 to 35,000 g/mol, U = (Mw/Mn)-1 is 1.3 to 2.3, B) copolycarbonates having a content of greater than 0 and less than 50 mol% of diphenol unit of the formula, based on the sum of the diphenols: for linear CoPC having an average molecular weight (weight-average) of from 16,000 to 35,000 g/mol, U = (Mw/Mn)-1 is 1.2 to 2.4; R 6 and R 7 independently of one another represent H, C 1 -C 18 -alkyl, C 1 -C 18 -alkoxy or halogen or represent aryl or aralkyl, each of which is optionally substituted, X represents C 1 - to C 6 -alkylene, C 2 - to C 5 -alkylidene or C 6 - to C 12 -arylene; A) copolycarbonates having a content of ≥ 50 mol% and < 100 mol% of diphenol unit of the formula, based on the sum of the diphenols: for linear CoPC having an average molecular weight (weight-average) of from 18,000 to 35,000 g/mol, U = (Mw/Mn)-1 is 1.3 to 2.3, for linear CoPC having an average molecular weight (weight-average) of from 18,000 to 35,000 g/mol, U = (Mw/Mn)-1 is 1.3 to 2.3, B) copolycarbonates having a content of greater than 0 and less than 50 mol% of diphenol unit of the formula, based on the sum of the diphenols: for linear CoPC having an average molecular weight (weight-average) of from 16,000 to 35,000 g/mol, U = (Mw/Mn)-1 is 1.2 to 2.4; for linear CoPC having an average molecular weight (weight-average) of from 16,000 to 35,000 g/mol, U = (Mw/Mn)-1 is 1.2 to 2.4;