In this contribution two modifications of the LM chroma process are proposed. The first modification consists in reducing the number of reference samples used to compute the cross-component linear model parameters to up to 6. The second modification consists in reducing the size of the table required to perform the division for computing the linear model parameters from 2×512 to 64. The first modification is reported to result in PSNR-Y, U, V BD-rate variations of 0.0%, 0.1%, 0.1% in AI configuration, 0.0%, 0.1%, 0.1% in RA configuration, while reducing the number of checks to derive the cross-component linear model parameters. The second modification is reported to in PSNR-Y, U, V BD-rate variations of 0.0%, 0.0%, 0.0% in AI configuration, 0.0%, 0.0%, 0.1% in RA configuration, while reducing the memory size from 2048 bytes to 128 bytes. The combination of both modifications results in PSNR-Y, U, V BD-rate variations of 0.0%, 0.1%, 0.1% in AI configuration, 0.0%, 0.0%, 0.0% in RA configuration. Additional results are reported to show that the table size can be further reduced, up to 8, without significant impact on the BD-rate performance.