We experimentally compare the output abilities of lightly and heavily doped Ti:Sapphire (Ti:S) amplifiers with diameters as large as 150 mm. Although a lightly doped Ti:S is more favorable to overcome parasitic lasing (PL) and transverse amplified spontaneous emission (TASE), the self-phase-modulation (SPM) effect becomes more pronounced when a longer crystal is used. Recompression of the amplified, stretched pulses can be seriously affected by the SPM effect. We then propose a temporal multi-pulse pump scheme to suppress PL and TASE in a thin, heavily doped Ti:S crystal. This novel temporal multi-pulse pump technique can find potential applications in 10 PW chirped-pulse amplification laser systems.