We report preliminary results obtained for solitary pulses in a discrete nonlinear Schroedinger (self-trapping) equation in an infinite domain by means of the variational approximation. We assume a certain ansatz for the pulse, following the pattern of the variational approximation for pulses in the continuum model. Using the conservation of the "number of quanta" (NOQ), we bring the evolution equations for free parameters of the ansatz to the Newton's equation of motion for a single degree of freedom (in a certain effective potential). At any value of the pulse's NOQ, the latter equation admits a single equilibrium position which corresponds to a stable stationary pulse. However, there is a definite threshold value of the NOQ such that above the threshold any initial configuration gets trapped into a stable pulse, while below the threshold the trapping takes place provided that the initial configuration is not too narrow, otherwise it will be spreading out indefinitely.