  We use higher-redshift gamma-ray burst (GRB), HII starburst galaxy (HIIG),
and quasar angular size (QSO-AS) measurements to constrain six spatially flat
and non-flat cosmological models. These three sets of cosmological constraints
are mutually consistent. Cosmological constraints from a joint analysis of
these data sets are largely consistent with currently-accelerating cosmological
expansion as well as with cosmological constraints derived from a combined
analysis of Hubble parameter ($H(z)$) and baryon acoustic oscillation (BAO,
with Planck-determined baryonic matter density) measurements. A joint analysis
of the $H(z)$ + BAO + QSO-AS + HIIG + GRB data provides fairly
model-independent determinations of the non-relativistic matter density
parameter $\Omega_{\rm m_0}=0.313\pm0.013$ and the Hubble constant
$H_0=69.3\pm1.2\ \rm{km \ s^{-1} \ Mpc^{-1}}$. These data are consistent with
the dark energy being a cosmological constant and with spatial hypersurfaces
being flat, but they do not rule out mild dark energy dynamics or a little
spatial curvature. We also investigate the effect of including quasar flux
measurements in the mix and find no novel conclusions.
