We investigate a soliton charge and energy transport in anharmonic molecular systems and show that at large enough anharmonicity parameter there are two kinds of envelope solitons, one of which is a Davydov soliton. It has the usual one-bell shape and may exist at any anharmonicity. The other kind has a two-bell shape. The two-bell shape is a bound state of Davydov and Boussinesq solitons. It is caused by excitation (electron) tunnelling in the effective lattice potential.