  An $A$-cellular space is a space built from $A$ and its suspensions,
analogously to the way that $CW$-complexes are built from $S^0$ and its
suspensions. The $A$-cellular approximation of a space $X$ is an $A$-cellular
space $CW_{A}X$ which is closest to $X$ among all $A$-cellular spaces. The
$A$-complexity of a space $X$ is an ordinal number that quantifies how
difficult it is to build an $A$-cellular approximation of $X$. In this paper,
we study spaces with low complexity. In particular we show that if $A$ is a
sphere localized at a set of primes then the $A$-complexity of each space $X$
is at most 1.
