We have studied the conditions resulting in maximum lowering of the excitation threshold for pulsed stimulated Raman (SRS) lasers. It has been shown theoretically that in order to achieve the lowest possible values of laser radiation pulse energy needed to excite lasing in SRS lasers, we need high reflection of the cavity mirrors and low losses at the wavelength of the 1st Stokes component, high reflection of the output mirror at the wavelength of the pump radiation, and also matching of the confocal parameters for the exciting laser radiation and the cavity with each other and with the length of the Raman-active medium. The experimentally achieved excitation threshold for an SRS laser based on a barium nitrate crystal was 6 μJ, which quantitatively corresponds well to the calculation results. Lasing of up to five Stokes components simultaneously occurred. The efficiency for conversion of the laser radiation to one component was as high as 39%.