  We studied the recall efficiency as a function of optical depth of rephased
amplified spontaneous emission (RASE), a protocol for generating entangled
light. The experiments were performed on the $^{3}\! H_{4}$ $\rightarrow$
$^{1}\! D_{2}$ transition in the rare-earth doped crystal
Pr$^{3+}$:Y$_{2}$SiO$_{5}$, using a four-level echo sequence between four
hyperfine levels to rephase the emission. Rephased emission was observed for
optical depths in the range of $\alpha L$ = 0.8 to 2.0 with a maximum rephasing
efficiency of 14 % observed while incorporating spin storage. This efficiency
is a significant improvement over the previously reported non-classical result
but is well short of the predicted efficiency. We discuss the possible
mechanisms limiting the protocol's performance, and suggest ways to overcome
these limits.
