A method of modulating digital signals for Discrete Multitone, DMT, transmission over a communications facility, comprising the steps of: bit loading of a plurality of subchannels; identifying at least one of the plurality of subchannels that is unloaded; receiving a payload bitstream; encoding the received payload bitstream into a plurality of symbols, the symbols each associated with one of the plurality of subchannels, the plurality of symbols arranged as a digital payload signal; for each of a plurality of phases corresponding to an upsampling function, forming (62; 92) a time-domain sum signal of the payload signal and a trial clip prevention signal, the trial clip prevention signal being orthogonal to the payload signal and associated with the at least one unloaded subchannel, and the trial clip prevention and payload signals having been filtered by a filter associated with the current phase; applying a function (64; 94) to the sum signal to derive a clipped sum signal; responsive to the clipped sum signal differing from the sum signal, modifying (68; 98) the trial clip prevention signal for the current phase; repeating (70; 100) the forming (62; 92), applying (64; 94), and modifying (68; 98) steps for each of the plurality of phases; responsive to the clipped sum signal having differed from the sum signal for any of the plurality of phases, repeating the forming (62; 92), applying (64;94), and modifying (68;98) steps for the plurality of phases; and responsive to the clipped sum signal not differing from the sum signal over all of the plurality of phases, processing a sum of the payload signal and the current trial clip prevention signal. bit loading of a plurality of subchannels; identifying at least one of the plurality of subchannels that is unloaded; receiving a payload bitstream; encoding the received payload bitstream into a plurality of symbols, the symbols each associated with one of the plurality of subchannels, the plurality of symbols arranged as a digital payload signal; for each of a plurality of phases corresponding to an upsampling function, forming (62; 92) a time-domain sum signal of the payload signal and a trial clip prevention signal, the trial clip prevention signal being orthogonal to the payload signal and associated with the at least one unloaded subchannel, and the trial clip prevention and payload signals having been filtered by a filter associated with the current phase; applying a function (64; 94) to the sum signal to derive a clipped sum signal; responsive to the clipped sum signal differing from the sum signal, modifying (68; 98) the trial clip prevention signal for the current phase; repeating (70; 100) the forming (62; 92), applying (64; 94), and modifying (68; 98) steps for each of the plurality of phases; responsive to the clipped sum signal having differed from the sum signal for any of the plurality of phases, repeating the forming (62; 92), applying (64;94), and modifying (68;98) steps for the plurality of phases; and responsive to the clipped sum signal not differing from the sum signal over all of the plurality of phases, processing a sum of the payload signal and the current trial clip prevention signal.