  We prove closure properties for the class of C*-algebras that are inductive
limits of semiprojective C*-algebras. Most importantly, we show that this class
is closed under shape domination, and so in particular under shape and homotopy
equivalence. It follows that the considered class is quite large. It contains
for instance the stable suspension of any nuclear C*-algebra satisfying the UCT
and with torsion-free $K_0$-group. In particular, the stabilized C*-algebra of
continuous functions on the pointed sphere is isomorphic to an inductive limit
of semiprojectives.
