Spam and Denial-of-Service (DoS) attacks are growing threats on the internet. Cryptographic puzzles can be used to address the problem effectively. Additionally, the Trusted Puzzle Solver (TPS), which is similar to the Trusted Platform Module (TPM), is also proposed to help constructing crypto puzzles that may have some outstanding specialties in security and efficiency. Based on the analysis and discussion of two existing crypto puzzles relying on the TPS with a trusted clock, two new improved crypto puzzles are presented, and all the drawbacks found in the old ones are eliminated.