All nonlinear dispersive wave equations in the general class are known to possess multi-peakon weak solutions. A classification is presented for families of multi-peakon equations in this class that possess conserved momentum; conserved H 1 norm of u; conserved H 2 norm of u; conserved L 2 norm of m; related conservation laws. The results yield, among others, two interesting wide families of equations: for which the H 1 norm of u is conserved; $\newcommand {\p}{\partial} m_t-\frac {1}{2} u_x h^{\prime}(u) m+(h (u) m) _x= 0$ for which the L 2 norm of m is conserved. The overlap of these two families yields a singular equation which is nevertheless found to possess both smooth solitary wave solutions and peakon travelling wave solutions.