We analyze the market efficiency of 25 commodity futures across various groups -- metals, energies, softs, grains and other agricultural commodities. To do so, we utilize recently proposed Efficiency Index to find that the most efficient of all the analyzed commodities is heating oil, closely followed by WTI crude oil, cotton, wheat and coffee. On the other end of the ranking, we detect live cattle and feeder cattle. The efficiency is also found to be characteristic for specific groups of commodities -- energy commodities being the most efficient and the other agricultural commodities (formed mainly of livestock) the least efficient groups. We also discuss contributions of the long-term memory, fractal dimension and approximate entropy to the total inefficiency. Last but not least, we come across the nonstandard relationship between the fractal dimension and Hurst exponent. For the analyzed dataset, the relationship between these two is positive meaning that local persistence (trending) is connected to global anti-persistence. We attribute this to specifics of commodity futures which might be predictable in a short term and locally but in a long term, they return to their fundamental price.