Flow thinning (FT) is a traffic protection mechanism for communication networks with variable link capacities, for example wireless networks. With FT, end-to-end traffic demands use dedicated logical tunnels, for example MPLS tunnels, whose nominal capacity is subject to thinning in order to follow fluctuations in link capacities availability. Moreover, instantaneous traffic of each demand is throttled at its originating node accordingly to the current total capacity available on the demands dedicated tunnels so that the network is always capable of carrying the admitted traffic. In this paper we deal with efficient, implementable versions of FT, referred to as AFT (affine FT) and QFT (quadratic FT). By deriving appropriate link availability state and path generation algorithms, we show how real-life network dimen-sioning problems for AFT/QFT can be efficiently treated using a proper characterization of the network link availability states. Results of a numerical study illustrate tractability of the cost minimization problems, and assess efficiency of AFT/QFT as compared with other protection mechanisms.