  A bargraph is a self-avoiding lattice path with steps $U=(0,1)$, $H=(1,0)$
and $D=(0,-1)$ that starts at the origin and ends on the $x$-axis, and stays
strictly above the $x$-axis everywhere except at the endpoints. Bargraphs have
been studied as a special class of convex polyominoes, and enumerated using the
so-called wasp-waist decomposition of Bousquet-M\'elou and Rechnitzer. In this
paper we note that there is a trivial bijection between bargraphs and Motzkin
paths without peaks or valleys. This allows us to use the recursive structure
of Motzkin paths to enumerate bargraphs with respect to several statistics,
finding simpler derivations of known results and obtaining many new ones. We
also count symmetric bargraphs and alternating bargraphs. In some cases we
construct statistic-preserving bijections between different combinatorial
objects, proving some identities that we encounter along the way.
