In order to improve the working performances of a transient Brillouin amplifier, the dependences of the signal-noise-ratio, sensitivity, energy extraction efficiency and signal amplification factor on exponential gain G are numerically studied based on the theoretical model of transient Brillouin amplification including distributed noise, and an optimal working point of a Brillouin amplifier is obtained. Experimental verifications are performed by choosing CS2 and FC-72 as nonlinear media. A frequency-doubled Nd:YAG pulse laser is used. Results show that when the pump pulse lags behind the Stokes signal pulse by an amount of time equal to half the pulse width, Gopt can be set to be above the SBS threshold exponential gain Gth. For a collinear Brillouin amplifier, Gopt is 1.1-1.3 times Gth; while for a non-collinear structure, Gopt can be set to be over 1.3 times Gth. Nearly saturated amplification is achieved.