  We offer some elementary characterisations of group and round quadratic
forms. These characterisations are applied to establish new (and recover
existing) characterisations of Pfister forms. We establish "going-up" results
for group and anisotropic round forms with respect to iterated Laurent series
fields, which contrast with the established results with respect to rational
function field extensions. For forms of two-power dimension, we determine when
there exists a field extension over which the form becomes an anisotropic group
form that is not round.
