We study certain filtrations of indecomposable injective modules over classical Lie superalgebras, applying a general approach for noetherian rings developed by Brown, Jategaonkar, Lenagan, and Warfield. To indicate the consequences of our analysis, suppose that
g
\mathfrak {g}
is a complex classical simple Lie superalgebra and that
E
E
is an indecomposable injective
g
\mathfrak {g}
-module with nonzero (and so necessarily simple) socle
L
L
. (Recall that every essential extension of
L
L
, and in particular every nonsplit extension of
L
L
by a simple module, can be formed from
g
\mathfrak {g}
-subfactors of
E
E
.) A direct transposition of the Lie algebra theory to this setting is impossible. However, we are able to present a finite upper bound, easily calculated and dependent only on
g
\mathfrak {g}
, for the number of isomorphism classes of simple highest weight
g
\mathfrak {g}
-modules appearing as
g
\mathfrak {g}
-subfactors of
E
E
.