  We discuss the determination of deep-inelastic hadron structure in lattice
QCD. By using a fictitious heavy quark, direct calculations of the Compton
scattering tensor can be performed in Euclidean space that allow the extraction
of the moments of structure functions. This overcomes issues of operator mixing
and renormalisation that have so far prohibited lattice computations of higher
moments. This approach is especially suitable for the study of the twist-two
contributions to isovector quark distributions, which is practical with current
computing resources. While we focus on the isovector unpolarised distribution,
our method is equally applicable to other quark distributions and to
generalised parton distributions. By looking at matrix elements such as
$<\pi^\pm| T [V^\mu(x) A^{\nu}(0)]|0>$ (where $V^\mu$ and $A^\nu$ are vector
and axial-vector heavy-light currents) within the same formalism, moments of
meson distribution amplitudes can also be extracted.
