We report NanoSIMS Si and Mg–Al isotopic data (and C, N, and Ti isotopic data, when available) for 85 submicron-to micron-sized presolar SiC grains from the CM2 Murchison meteorite, including 60 mainstream (MS), 8 AB1, 8 X, 7 AB2, and 2 Y grains. The MS and Y grain data demonstrate that (1) C and N contamination mainly appears as surface contamination, and sufficient presputtering is needed to expose a clean grain surface for obtaining intrinsic C and N signals, and (2) Mg and Al contamination appears as adjacent grains and rims, and high-resolution imaging and the choice of small regions of interest during data reduction together are effective in suppressing the contamination. Our results strongly indicate that previous studies of presolar SiC grains could have sampled differing degrees of contamination for C, N, Mg, and Al. Compared to the literature data, our new MS and Y grains are in better agreement with carbon star observations for both the C and N isotopic ratios. By comparing our new, tighter distributions of 12 C/13 C, 14 N/15 N, and initial 26 Al/27 Al ratios for MS and Y grains with FRUITY low-mass asymptotic giant branch (AGB) stellar models, we provide more stringent constraints on the occurrence of cool bottom processing and the production of 26 Al in N-type carbon stars, which are classical AGB stars.