  We have investigated the information content in reflected-starlight spectra
of exoplanets. We specify our analysis to Barnard's Star b candidate
super-Earth, for which we assume a radius 0.6 times that of Neptune, an
atmosphere dominated by H$_2$-He, and a CH$_4$ volume mixing ratio of
5$\cdot$10$^{-3}$. The main conclusions of our study are however
planet-independent. We set up a model of the exoplanet described by seven
parameters including its radius, atmospheric methane abundance and basic
properties of a cloud layer. We generate synthetic spectra at zero phase (full
disk illumination) from 500 to 900 nm and spectral resolution R$\sim$125-225.
We simulate a measured spectrum with a simplified, wavelength-independent noise
model at Signal-to-Noise ratio S/N=10. With an MCMC-based retrieval
methodology, we analyse which planet/atmosphere parameters can be inferred from
the measured spectrum and the theoretical correlations amongst them. We
consider limiting cases in which the planet radius is either known or
completely unknown, and intermediate cases in which the planet radius is partly
constrained. If the planet radius is known, we can generally discriminate
between cloud-free and cloudy atmospheres, and constrain the methane abundance
to within two orders of magnitude. If the planet radius is unknown, new
correlations between model parameters occur and the accuracy of the retrievals
decreases. Without a radius determination, it is challenging to discern whether
the planet has clouds, and the estimates on methane abundance degrade. However,
we find the planet radius is constrained to within a factor of two for all the
cases explored. Having a priori information on the planet radius, even if
approximate, helps improve the retrievals. We urge exoplanet detection efforts
to extend the population of long-period planets with mass and radius
determinations.
