We present a new accuracy condition for constructing mass-lumped elements. This condition is less restrictive than the one previously used and enabled us to construct new mass-lumped tetrahedral elements for 3D wave propagation modelling. The new degree-2 and degree-3 elements require significantly fewer nodes than previous versions and mass-lumped tetrahedral elements of higher degree had not been found before. We also present a new accuracy condition for evaluating the stiffness matrix-vector product. This enabled us to obtain tailored quadrature rules for the new elements that further reduce the computational cost.@en