Motivated by the information transmission in neurons with various applications in in-vivo nano-machines or emerging medical applications, Ye and Elishco [2023] introduced a communication channel, called the absorption channel, and proposed codes correcting absorption errors. For a non-binary alphabet $\Sigma_q$, the authors presented constructions of codes of length $n$ correcting a single absorption and the best construction yielded a redundancy of $\log_q n + 12 \log_q \log_q n + O(1)$ symbols. In this work, we make progress on the code design problem above and show that the redundancy can be further reduced significantly as follows: • When $q = 3$, we construct “nearly optimal” ternary codes of length $n$ with at most $\log_3 n + 5.43$ redundant symbols. Note that such a redundancy is optimal up to a constant. • For a general alphabet $\Sigma_q$, we construct q-ary codes of length $n$ correcting a single absorption error with $\log_q n + 3 \log_q \log_q n + O(1)$ redundant symbols, providing an alternative simpler construction that improves the results given by Ye and Elishco.