  We give several Bishop-Gromov relative volume comparisons with integral Ricci
curvature which improve the results in \cite{PW1}. Using one of these volume
comparisons, we derive an estimate for the volume entropy in terms of integral
Ricci curvature which substantially improves an earlier estimate in \cite{Au2}
and give an application on the algebraic entropy of its fundamental group. We
also extend the almost minimal volume rigidity of \cite{BBCG} to integral Ricci
curvature.
