Very high bit-rate digital subscriber line (VDSL) is the latest generation in the ongoing evolution of DSL standards. VDSL aims at bringing truly broadband access, greater than 52 Mbps in the downstream, to the mass consumer market. This is achieved by transmitting in frequencies up to 12 MHz. Operating at such high frequencies gives rise to crosstalk between the DSL systems in a binder, limiting achievable data-rates. Crosstalk is typically 10-15 dB larger than other noise sources and is the primary limitation on performance in VDSL. In downstream transmission several crosstalk precompensation schemes have been proposed to address this issue. Whilst these schemes lead to large performance gains, they also have extremely high complexities, beyond the scope of current implementation. In this paper we develop the concept of partial crosstalk precompensation. The majority of the crosstalk experienced in a DSL system comes from only a few other lines within the binder. Furthermore its effects are limited to a small subset of tones. Partial precompensation exploits this by limiting precompensation to the tones and lines where it gives maximum benefit. As a result, these schemes achieve the majority of the gains of full crosstalk precompensation at a fraction of the run-time complexity. In this paper we develop several partial precompensation schemes. We show that with only 20% of the run-time complexity of full precompensation it is possible to achieve 80% of the performance gains