  We use CMB (WMAP and ACBAR), large scale structure (SDSS luminous red
galaxies) and supernova (SNLS) data to constrain the possible contribution of
CDM isocurvature modes to the primordial perturbation spectrum. We consider
three different admixtures with adiabatic modes in a flat $\Lambda$CDM
cosmology with no tensor modes: fixed correlations with a single spectral
index; general correlations with a single spectral index; and general
correlations with independent spectral indices for each mode. For fixed
correlations, we verify the WMAP analysis for fully uncorrelated and
anti-correlated modes, while for general correlations with a single index we
find a small tightening of the constraint on the fractional contribution of
isocurvature modes to the observed power over earlier work. For
generally-correlated modes and independent spectral indices our results are
quite different to previous work, needing a doubling of prior space for the
isocurvature spectral index in order to explore adequately the region of high
likelihood. Standard Markov-Chain Monte-Carlo techniques proved to be
inadequate for this particular application; instead our results are obtained
with nested sampling. We also use the Bayesian evidence, calculated simply in
the nested-sampling algorithm, to compare models, finding the pure adiabatic
model to be favoured over all our isocurvature models. This favouring is such
that the logarithm of the Bayes Factor, $\mathrm{ln} B < -2$ for all models and
$\mathrm{ln} B < -5$ in the cases of fully anti-correlated modes with a single
spectral index (the curvaton scenario) and generally-correlated modes with a
single spectral index.

Cosmology and Nongalactic Astrophysics