  H1 has measured the diffractive DIS cross section $ep \rightarrow eXY$ using
data from both of the HERA data-taking periods. Using new measurements of the
diffractive cross section at different centre-of-mass energies, the diffractive
longitudinal structure function $F_L^D$ has been extracted. The results are in
agreement with NLO QCD predictions based on fits to inclusive data. New high
statistics measurements of the diffractive reduced cross section $\sigma_r^D$
have been made using two experimental methods covering the accessible kinematic
range. This precise dataset agrees well with QCD-based predictions.
