  For area-preserving H\'enon-like maps and their compositions, we consider
smooth perturbations that keep the reversibility of the initial maps but
destroy their conservativity. For constructing such perturbations, we use two
methods, the original method based on reversible properties of maps written in
the so-called cross-form, and the classical Quispel-Roberts method based on a
variation of involutions of the initial map. We study symmetry breaking
bifurcations of symmetric periodic points in reversible families containing
quadratic conservative orientable and nonorientable H\'enon maps as well as the
product of two asymmetric H\'enon maps (with the Jacobians $b$ and $b^{-1}$).
