  The pebbling number of a graph $G$, $f(G)$, is the least $p$ such that,
however $p$ pebbles are placed on the vertices of $G$, we can move a pebble to
any vertex by a sequence of moves, each move taking two pebbles off one vertex
and placing one on an adjacent vertex. It is conjectured that for all graphs
$G$ and $H$, $f(G\times H)\leq f(G)f(H)$. If the graph $G$ satisfies the odd
two-pebbling property, we will prove that $f(C_{4k+3}\times G)\leq
f(C_{4k+3})f(G)$ and $f(M(C_{2n})\times G)\leq f(M(C_{2n}))f(G)$, where
$C_{4k+3}$ is the odd cycle of order $4k+3$ and $M(C_{2n})$ is the middle graph
of the even cycle $C_{2n}$.
