  We investigate the bi-orderability of two-bridge knot groups and the groups
of knots with 12 or fewer crossings by applying recent theorems of Chiswell,
Glass and Wilson. Amongst all knots with 12 or fewer crossings (of which there
are 2977), previous theorems were only able to determine bi-orderability of 599
of the corresponding knot groups. With our methods we are able to deal with 191
more.
