In this paper, we present a very fast and accurate rectilinear Steiner minimal tree (RSMT) algorithm called fast lookup table estimation (FLUTE). FLUTE is based on a precomputed lookup table to make RSMT construction very fast and very accurate for low-degreeThe degree of a net is the number of pins in the net. nets. For high-degree nets, a net-breaking technique is proposed to reduce the net size until the table can be used. A scheme is also presented to allow users to control the tradeoff between accuracy and runtime. FLUTE is optimal for low-degree nets (up to degree 9 in our current implementation) and is still very accurate for nets up to degree 100. Therefore, it is particularly suitable for very large scale integration applications in which most nets have a degree of 30 or less. We show experimentally that, over 18 industrial circuits in the ISPD98 benchmark suite, FLUTE with default accuracy is more accurate than the Batched 1-Steiner heuristic and is almost as fast as a very efficient implementation of Prim's rectilinear minimum spanning tree algorithm.