Within QCD, colourless states may be constructed corresponding to exotic matter outside of the traditional quark model. Experiments have recently observed tetraquark and pentaquark states, but no definitive hybrid meson signals have been observed. With the construction of the PANDA experiment at FAIR, and with full commissioning of the GlueX experiment at JLab expected to be completed this year, the opportunity for the observation of hybrid mesons has greatly increased. However, theoretical calculations are necessary to ascertain the identity of any experimental resonances that may be observed. We present selected QCD sum rule results from a full range of quantum numbers for open-flavour hybrid mesons with heavy valence quark content, including non-perturbative condensate contributions up to six-dimensions.