  Let $\mathbb{N}_0$ denote the set of all non-negative integers and
$\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-indexer
(IASI) of a given graph $G$ is an injective function $f:V(G)\to
\mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to
\mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also
injective. An IASI $f$ of a graph $G$ is said to be a weak IASI of $G$ if
$|f^+(uv)|=\max(|f(u)|,|f(v)|)$ for all $u,v\in V(G)$. A graph which admits a
weak IASI may be called a weak IASI graph. The sparing number of a graph $G$ is
the minimum number of edges with singleton set-labels required for a graph $G$
to admit a weak IASI. In this paper, we introduce the notion of $k$-sieve
graphs of a given graph and study their sparing numbers.
