We release 70 small and discriminative test sets for machine translation (MT) evaluation called variance-aware test sets (VAT), covering 35 translation directions from WMT16 to WMT20 competitions. VAT is automatically created by a novel variance-aware filtering method that filters the indiscriminative test instances of the current MT benchmark without any human labor. Experimental results show that VAT outperforms the original WMT benchmark in terms of the correlation with human judgment across mainstream language pairs and test sets. Further analysis on the properties of VAT reveals the challenging linguistic features (e.g., translation of low-frequency words and proper nouns) for the competitive MT systems, providing guidance for constructing future MT test sets. The test sets and the code for preparing variance-aware MT test sets are freely available at https://github.com/NLP2CT/Variance-Aware-MT-Test-Sets.