Luby Transform (LT) codes are the first practical implementation of digital fountain codes. In LT codes, encoding symbols are independently generated so as to realize the universal property which means that performance is independent of channel parameters. The universal property makes LT codes able to provide reliable delivery simultaneously via channels of different quality while it may also limit the flexibility of LT codes. In certain application scenarios, such as real-time multimedia transmission, most receivers have tolerable channels whose erasure rates are not fixed, and channels of high erasure rate are outside the design box. In this paper, Connection Choice (CC) codes are proposed to trade the universal property for better performance. The key to CC codes is replacement of random selection with tournament selection. Tournament selection can equalize the frequency of input symbols to join encoding and change the degree distribution of input symbols. Our study indicates that CC codes with appropriate degree distributions provide better performance than the best known LT code when channels of high erasure rate can be ignored. CC codes enable system designers to customize digital fountain codes by taking into account the distribution of the erasure rate and create a new possibility for setting trade-offs between performance and erasure rate.