Local mutual-information privacy (LMIP) is a privacy notion that aims to quantify the reduction of uncertainty about the input data when the output of a privacy-preserving mechanism is revealed. We study the relation of LMIP with local differential privacy (LDP), the de facto standard notion of privacy in context-independent (CI) scenarios, and with local information privacy (LIP), the state-of-the-art notion for context-dependent settings. We establish explicit conversion rules, i.e., bounds on the privacy parameters for an LMIP mechanism to also satisfy LDP/LIP, and vice versa. We use our bounds to formally verify that LMIP is a weak privacy notion. We also show that uncorrelated Gaussian noise is the best-case noise in terms of CI-LMIP if both the input data and the noise are subject to an average power constraint.