A cover free family (CFF) is a useful mathematical tool for cryptographic schemes where any pre-defined number of sets in the family do not cover another set in the family. The common disadvantage of CFF-based schemes is the requirement for a significantly large amount of data such as public keys and ciphertexts. This paper proposes a simple method to reduce the size of ciphertexts in CFF-based broadcast encryption schemes by removing redundant elements from sets in the family, and then analyzes the size of cihpertexts. As a result, in a typical distribution case, the average amount of ciphertexts is reduced to 83 percents (from 691Kbits to 576Kbits).