  We examine the influence of a continuous density structuring transverse to
coronal slabs on the dispersive properties of fundamental standing kink and
sausage modes supported therein. We derive generic dispersion relations (DRs)
governing linear fast waves in pressureless straight slabs with general
transverse density distributions, and focus on the cases where the density
inhomogeneity takes place in a layer of arbitrary width and in arbitrary form.
The physical relevance of the solutions to the DRs is demonstrated by the
corresponding time-dependent computations. For all profiles examined, the
lowest-order kink modes are trapped regardless of longitudinal wavenumber $k$.
A continuous density distribution introduces a difference to their periods of
$\lesssim 13\%$ when $k$ is the observed range, relative to the case where the
density profile takes a step-function form. Sausage modes and other branches of
kink modes are leaky at small $k$, and their periods and damping times are
heavily influenced by how the transverse density profile is prescribed, the
lengthscale in particular. These modes have sufficiently high quality to be
observable only for physical parameters representative of flare loops. We
conclude that while the simpler DR pertinent to a step-function profile can be
used for the lowest-order kink modes, the detailed information on the
transverse density structuring needs to be incorporated into studies of sausage
modes and higher-order kink modes.
