Tweet Timeline Generation (TTG) systems provide users with informative and concise summaries of topics, as they developed over time, in a retrospective manner. In order to produce a tweet timeline that constitutes a summary of a given topic, a TTG system typically retrieves a list of potentially-relevant tweets over which the timeline is eventually generated. In such design, dependency of the performance of the timeline generation step on that of the retrieval step is inevitable. In this work, we aim at improving the performance of a given timeline generation system by controlling the depth of the ranked list of retrieved tweets considered in generating the timeline. We propose a supervised approach in which we predict the optimal depth of the ranked tweet list for a given topic by combining estimates of list quality computed at different depths. We conducted our experiments on a recent TREC TTG test collection of 243M tweets and 55 topics. We experimented with 14 different retrieval models (used to retrieve the initial ranked list of tweets) and 3 different TTG models (used to generate the final timeline). Our results demonstrate the effectiveness of the proposed approach; it managed to improve TTG performance over a strong baseline in 76% of the cases, out of which 31% were statistically significant, with no single significant degradation observed.