Compact-like discrete breathers in discrete one-dimensional monatomic chains are investigated by discussing a generalized discrete one-dimensional monatomic model. It is proven that compact-like discrete breathers exist not only in soft φ4 potential but also in hard φ4 potential and K4 chains. The measurements of compact-like discrete breathers core in soft and hard φ4 potential are determined by coupling parameter K4, while the measurements of compact-like discrete breathers core in K4 chains are not related to coupling parameter K4. The stabilities of compact-like discrete breathers correlate closely to coupling parameter K4 and the boundary condition of lattice.