Besides CPI and core CPI, we also have 16% trimmed-mean CPI and median CPI. They are alternative ways to measure core CPI (CPI excluding food and energy).
16% trimmed-mean CPI is a weighted average of inflation that excludes 8% of the CPI components with the highest and lowest monthly price changes respectively.
Median CPI on the other hand is the inflation rate of the component at the median of the price change distribution.
In some respects median CPI and 16% trimmed-mean CPI are improved measures of core inflation when prices are especially volatile.
Both are still quite elevated these days, which supports the Fed's decision to keep tightening (shown are the annualized rates, not the monthly rates).