Yesterday, Attorney General Loretta Lynch made the unprecedented announcement that five of the world’s largest banks – JP Morgan, Citi, Barclays, RBS, and UBS – would be pleading guilty to criminal charges. According to the allegations, traders and executives working at the banks’ foreign exchange (FOREX) desks colluded through the use of chat rooms to fix currency prices on a daily basis. The fines are in the hundreds of millions, with Barclays total penalty (including those levied by US and UK authorities) at $2.4 billion topping the charts and Citigroup’s $925 million following behind. According to Assistant Attorney General Leslie Caldwell, these guilty pleas “communicate loud and clear that we will hold financial institutions accountable for criminal misconduct.”

But do they? Can they? In the world of “too big to fail,” JP MorganChase and Citigroup are whales among whales. Dodd-Frank, with its “living will” provision, was supposed to end too big to fail by requiring that systemically important financial institutions (SIFIs) create a plan for an orderly unwinding in the case of failure. But this provision contains the seeds of its own destruction. By designating firms as SIFIs, the government has made the too big to fail designation explicit when it was previously only implicit.

If a SIFI behaves badly, even very very badly (and there is no doubt that, if the allegations are true, the FOREX traders at these banks behaved badly indeed), how much can it be punished? While corporations can be held criminally liable, you obviously cannot imprison a corporation. Instead, criminal penalties for companies mean two things: (1) public censure and (2) fines. The big banks are not very popular these days and it’s unlikely the taint of public censure will cause much additional pain.

So that leaves the government with fines. For a fine to be a punishment, it must be large enough to hurt. These fines are not small. Even for a bank as large as Citi, $925 million is a chunk of change. But in imposing these fines, the government must walk a fine line. If Citi is a SIFI, can the government risk imposing a fine large enough that it risks destabilizing the entire company? Almost certainly not.

Complicating the government’s position is the fact that three of the banks – RBS, Barclays, and UBS – are foreign (RBS and Barclays are British, and UBS is Swiss). These banks have large footprints in the U.S. markets but, even if they were to falter, the government would be hard-pressed to offer a bailout even if it wanted to. Consider what happened during the financial crisis. Several large foreign banks were put at risk when AIG failed. Because the U.S. government could not, for political reasons if for no other, directly bail out these banks (even though their failure would impact U.S. markets), it instead engineered the so-called “back door bailout” by which TARP funds injected into AIG wound up in the hands of foreign banks. If the Department of Justice were to impose a heavy enough fine on RBS, Barclays, and UBS today that it really hurt those banks, that is, that it put any significant part of their business at risk, it could harm U.S. markets.

Secret price-fixing is bad. It distorts markets and prevents them from performing one of their most essential functions: price discovery. But having doubled-down on the too big to fail designation, the government has put itself into an impossible situation when it comes to reining in SIFIs’ bad behavior.