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Crosstalk (XT) is the main performance limiter in digital subscriber line (DSL) systems such as very-high-bit-rate digital subscriber line (VDSL) systems. In order to overcome these limitations various XT cancellation techniques have been proposed to mitigate this effect. While leading to very high performance gains, the computational complexity grows quadratically with the number of lines in a binder. This motivates partial cancellation schemes, maximising the capacity based on a given computational complexity. However, the data rate increase could still be very high above the quality of service (QoS) requirements that must be enforced for each user, leading to a `waste` of computational resources. Therefore a QoS-based partial cancellation algorithm is presented in this study which selects the lines to be cancelled based on the desired data rates of the users. It relies on partial zero-forcing XT cancellation but the used selection algorithm [QoS-based joint tone-line selection (QoS-JTLS)] aims at QoS fulfilment instead of data rate maximisation. Simulation results show that compared with other QoS-based algorithms and conventional selection algorithms, QoS-JTLS leads to better fulfilment of QoS demands for the same given computational complexity. In other words, the computational complexity needed to achieve the target data rates of the users is reduced when applying QoS-JTLS.