It has been recently shown that a sequence of R=q(M-1) redundancy free trellis stages of a recursive convolutional decoder can be compressed in a sequence of L=M-1 trellis stages, where M is the number of states of the trellis and q is a positive integer. In this paper, we show that for an M state Turbo decoder, among the L compressed trellis stages, only m = 3 or even m = 2 are necessary. The so-called $m$-min algorithm can either be used to increase the throughput for decoding a high rate turbo-code and/or to reduce its power consumption.