  A novel thermodynamic integration (TI) scheme is presented to compute the
crystal-liquid interfacial free energy ($\gamma_{\rm cl}$) from molecular
dynamics simulation. The scheme is applied to a Lennard-Jones system. By using
extremely short-ranged and impenetrable Gaussian flat walls to confine the
liquid and crystal phases, we overcome hysteresis problems of previous TI
schemes that stem from the translational movement of the crystal-liquid
interface. Our technique is applied to compute $\gamma_{\rm cl}$ for the (100),
(110) and (111) orientation of the crystalline phase at three temperatures
under coexistence conditions. For one case, namely the (100) interface at the
temperature $T=1.0$ (in reduced units), we demonstrate that finite-size scaling
in the framework of capillary wave theory can be used to estimate $\gamma_{\rm
cl}$ in the thermodynamic limit. Thereby, we show that our TI scheme is not
associated with the suppression of capillary wave fluctuations.
