The concept of time-memory trade-off was introduced in 1980 by Martin Hellman to conduct brute-force attacks against DES. The method consists of an intensive precomputation phase whose results are stored in tables, and subsequently used to significantly reduce the time required by the brute-force. An important improvement is the introduction in 2003 of rainbow tables by Philippe Oechslin. However, the process of precomputing rainbow tables is rather inefficient, primarily due to the high rate of computed values that are eventually discarded. Avoine, Carpent, and Leblanc-Albarel introduced in 2023 the descending stepped rainbow tables, which consists in recycling chains during the precomputation phase. In this paper, a new variant called ascending stepped rainbow tables is introduced. Formulas to predict attack time, precomputation time, memory requirements, and coverage are provided. Through theoretical results and implementation, the analysis demonstrates that this new variant offers significant improvements over both descending stepped rainbow tables and vanilla rainbow tables for high coverage. Specifically, for the typical 99.5% coverage, the precomputation time of ascending stepped rainbow tables is (up to) 30% faster than descending stepped tables, and (up to) 45% faster than vanilla rainbow tables, while also reducing the attack time up to 15% and 11%, respectively.