A sketch is a probabilistic data structure used to record frequencies of items in a multi-set. Sketches are widely used in various fields, especially those that involve processing and storing data streams. In streaming applications with high data rates, a sketch "fills up" very quickly. Thus, its contents are periodically transferred to the remote collector, which is responsible for answering queries. In this paper, we propose a new sketch, called Slim-Fat (SF) sketch, which has a significantly higher accuracy compared to prior art, a much smaller memory footprint, and at the same time achieves the same speed as the best prior sketch. The key idea behind our proposed SF-sketch is to maintain two separate sketches: a small sketch called Slim-subsketch and a large sketch called Fat-subsketch. The Slim-subsketch is periodically transferred to the remote collector for answering queries quickly and accurately. The Fat-subsketch, however, is not transferred to the remote collector because it is used only to assist the Slim-subsketch during the insertions and deletions and is not used to answer queries. We implemented and extensively evaluated SF-sketch along with several prior sketches and compared them side by side. Our experimental results show that SF-sketch outperforms the most widely used CM-sketch by up to 33.1 times in terms of accuracy. We have released the source codes of our proposed sketch as well as existing sketches at Github. The short version of this paper will appear in ICDE 2017.