Maintaining high degree of customer satisfaction is important for any corporation, which involves the customer support process. One important factor in this work is to keep customers' wait time for a reply at levels that are acceptable to them. In this study we investigate to what extent models trained by the Random Forest learning algorithm can be used to predict e-mail time-to-respond time for both customer support agents as well as customers. The data set includes 51,682 customer support e-mails of various topics from a large telecom operator. The results indicate that it is possible to predict the time-to-respond for both customer support agents (AUC of 0.90) as well as for customers (AUC of 0.85). These results indicate that the approach can be used to improve communication efficiency, e.g. by anticipating the staff needs in customer support, but also indicating when a response is expected to take a longer time than usual. Copyright © 2020 by SCITEPRESS - Science and Technology Publications, Lda. All rights reserved.