  JWST observations indicate a surprising excess of luminous galaxies at $z\sim
10$ and above, consistent with efficient conversion of the accreted gas into
stars, unlike the suppression of star formation by feedback at later times. We
show that the high densities and low metallicities at this epoch {\it
guarantee} a high star-formation efficiency (SFE) in the most massive
dark-matter haloes. Feedback-free starbursts (FFBs) occur when the free-fall
time is shorter than $\sim 1$ Myr, below the time for low-metallicity massive
stars to develop winds and supernovae. This corresponds to a characteristic
density of $\sim 3\times 10^3$cm$^{-3}$. A comparable threshold density permits
a starburst by allowing cooling to star-forming temperatures in a free-fall
time. The galaxies within $\sim 10^{11} M_\odot$ haloes at $z \sim 10$ are
expected to have FFB densities. The halo masses allow efficient gas supply by
cold streams in a halo crossing time $\sim 80$ Myr. The FFBs gradually turn all
the accreted gas into stars in clusters of $\sim 10^{4-7} M_\odot$ within
galaxies that are rotating discs or shells. The starbursting clouds are
insensitive to radiative feedback and are shielded against feedback from
earlier stars. We predict high SFE above thresholds in redshift and halo mass,
where the density is $10^{3-4}$cm$^{-3}$. The $z\sim 10$ haloes of $\sim
10^{10.8} M_\odot$ are predicted to host galaxies of $\sim 10^{10} M_\odot$
with SFR $\sim 65 M_\odot$ yr$^{-1}$ and sub-kpc sizes. The metallicity is
$\leq 0.1 Z_\odot$ with little gas, dust, outflows and hot circumgalactic gas,
allowing a top-heavy IMF but not requiring it. The compact galaxies with
thousands of young FFB clusters may have implications on reionization,
black-hole growth and globular clusters.
