Grand juries have long held some of the criminal justice system's best-kept secrets. But their private process has come under extraordinary public scrutiny after recent decisions not to indict police in the deaths of unarmed men.

New York Gov. Andrew Cuomo last week proposed a limited lifting of the grand jury veil when police kill unarmed civilians. This week, a New York City judge will consider whether to release transcripts of a grand jury's investigation into Eric Garner's chokehold death.

Proposals to replace grand juries with preliminary hearings in open court, at least in some police killing cases, have recently been floated by lawmakers in Washington and Missouri.

But calls for more transparency have mixed with caution about doing away with the secrecy that can safeguard witnesses and the accused.