Before the removal of the "No Double Jeopardy" rule, the only way to deal with an accused who is found "not guilty" and then admits to committing the offence (and there are some who find the need to brag about beating the system) or if some compelling new evidence comes to light, was to try them for perjury, which carries (often) a shorter sentence than the crime for which they were originally tried.
Surely it would have been easier (and less contraversial), instead of removing an age old protection, to expand the purjury sentencing rules such that an offence of perjury carries the same maximum sentence as the original trial could have awarded (ie: A possible "life" maximum in the case of a murder charge).

Walrus