Machine-learning algorithms are improving and automating important functions in medicine, transportation, and business. Government officials have also started to take notice of the accuracy and speed that such algorithms provide, increasingly relying on them to aid with consequential public-sector functions, including tax administration, regulatory oversight, and benefits administration. [---] Can algorithmic governance be squared with legal principles of governmental transparency? We analyze this question and conclude that machine-learning algorithms' relative inscrutability does not pose a legal barrier to their responsible use by governmental authorities. [---]