  New observations of 11 compact galaxies in the 12CO J=2-1 and J=3-2
transitions and literature data have been used to construct accurate line
ratios in matched beams allowing LVG modelling of physical parameters. Fitting
a single gas component to observed line ratios tends to produce physically
unrealistic results, and is often not possible at all. Much better results are
obtained by modelling two distinct gas components. The molecular gas is usually
warm (T(kin)=50-150 K) and at least partially dense (n(H2)>3000 cm3). Most of
the gas-phase carbon in these galaxies is in atomic form; only a small fraction
(5%) is in carbon monoxide. Beam-averaged CO column densities are low,
typically 10(16) cm2 but molecular hydrogen column densities are high, of the
order of 10(22) cm2 and confirm large CO-to-H2 conversion factors, typically X
= 10(21)-10(22) cm2(K kms-1) found in low-metallicity environments by other
methods. From CO spectroscopy, three different types of molecular environment
are distinguished in compact galaxies. Type I (high rotational and isotopic
ratios) corresponds to hot and dense molecular clouds dominated by star-forming
regions. Type II has lower ratios, similar to the mean found for
infrared-luminous galaxies in general, and corresponds to environments engaged
in, but not dominated by, star-forming activity. Type III, characterized by low
12CO (2--1)/(1--0) ratios, corresponds to mostly inactive environments of
relatively low density.
