Tumour hypoxia is one of the limiting factors in obtaining tumour control in radiotherapy. The high-LET region of a beam of heavy charged particles such as carbon ions is located in the distal part of the Bragg peak. A modulated or spread out Bragg peak (SOBP) is a weighted function of several Bragg peaks at various energies, which however results in a dilution of the dose-average LET in the target volume. Here, we investigate the possibility to redistribute the LET by dedicated treatment plan optimisation, in order to maximise LET in the target volume. This may be a strategy to potentially overcome hypoxia along with dose escalation or dose painting. The high-LET region can be shaped in very different ways, while maintaining the distribution of the absorbed dose or biological effective dose. Treatment plans involving only carbon ion beams, show very different LET distributions depending on how the fields are arranged. Alternatively, a LET boost can be applied in multi-modal treatment planning, such as combining carbon ions with protons and/or photons. For such mixed radiation modalities, significant "LET boosts" can be achieved at nearly arbitrary positions within the target volume. Following the general understanding of the relationship between hypoxia, LET and the oxygen enhancement ratio (OER), we conclude, that an additional therapeutic advantage can be achieved by confining the high-LET part of the radiation in hypoxic compartments of the tumour, and applying low-LET radiation to the normoxic tissue. We also anticipate that additional advantages may be achieved by deliberate sparing of normal tissue from high LET regions. Consequently, treatment planning based on simultaneous dose and LET optimisation has a potential to achieve higher tumour control and/or reduced normal tissue control probability (NTCP).