Europe agreed to give Greece a new round of pain on Wednesday.

No doubt many of the power centers in Europe would call it debt relief. The Eurogroup — an informal body of representatives from the eurozone nations who coordinate economic policy with the European Central Bank — issued a statement on Wednesday welcoming the agreement. The president of the Eurogroup hailed it as a "breakthrough."

But it's not, both for a purely practical reason and a much deeper contextual one.

The practical reason is that it simply isn't big enough. Just last week, the International Monetary Fund (IMF), one of Greece's creditors and a participant in the negotiations, released a report that Greece's debt service payments were on course to eat up 60 percent of the country's gross domestic product (GDP) by 2060, and unemployment would stay above 12 percent until 2040. To prevent those projections from becoming reality, the IMF recommended delaying all of Greece's payments on its principal until 2045 or 2055, and fixing its interest payments at 1.5 percent until then.

Wednesday's agreement is to provide Greece with a new bailout of $11.5 billion, to be doled out in stages starting in June, in exchange for yet another round of spending cuts and tax hikes from Greece. Some form of debt relief will be phased in starting in 2018. According to The Wall Street Journal, the Eurogroup president said, "Among the steps that will be considered in 2018 are caps and deferrals on interest rates as well as the return to Athens of profits from Greek government bonds held by eurozone central banks."

So it will be another round of the infuse-Greece-with-money-and-promptly-drain-it-again doom loop of the last few years. Then some more debt-relief-mumble in 2018. This is obviously nowhere near equal to the scale of the challenge as the IMF described it.

But I also mentioned that deeper contextual problem. And that line about "the return to Athens of profits from Greek government bonds held by eurozone central banks" gets to the heart of it.

Here's the way the division between the Federal Reserve — the U.S. central bank — and the federal government works in America. The federal government sets fiscal policy — taxation and spending — and if it spends more than it taxes, it issues new debt bonds. The Fed, in turn, has the power to print all the U.S. dollars it likes, and to use that power to buy those bonds off the financial markets. So the Fed can finance the government's borrowing almost indefinitely — the risk of high inflation is the only upper bound.

But fundamentally, the Fed and the federal government are part of the same conglomerate entity. The Fed was created by Congress, after all. More to the point, the Fed remits all profits it makes (after paying its labor and operating costs) on its portfolio of assets right back to the Federal Treasury as revenue — a record $97.7 billion in 2015. So the government pays the Fed interest on the U.S. debt the Fed holds, and then the Fed gives it right back to the government.

When the Fed buys U.S. debt, that debt is removed from the financial markets and the government stops losing money on it. It's de facto debt relief — for all intents and purposes, the debt ceases to exist as long as the Fed holds it.

It's similar in the eurozone. The European Central Bank (ECB) oversees all the national central banks in the eurozone, and it has the power to create euros and buy up the bonds of the eurozone nations, same as the Fed can create U.S. dollars and buy up U.S. debt. And like the Fed, the ECB takes the interest it earns on all those bonds and other assets and gives them right back to the eurozone governments. But since it's doing this across multiple nations, and not just one, how to distribute that revenue is tricky. The ECB has chosen to keep Greece in the loop in the past. But the fact that the Eurogroup is including it as a form of debt relief highlights that whether Greece gets included is a fundamentally political decision.

Meanwhile, the system has cut Greece out of the loop in other ways. Like the Fed, the ECB has also done quantitative easing (QE): created a bunch of money, and used it to buy up bonds and assets to goose the economy. Remember, the is de facto debt relief — the ECB buys a eurozone nation's debt, and the nation gets the interest it pays on it right back. And the ECB had bought at least 136.5 billion euros in French debt, 117.7 billion in Italian debt, and a whopping 171.8 billion in German debt since early 2015, for example. For some of the eurozone countries, the total debt relief will be over 10 percent of their GDP.

But the ECB hasn't included Greek debt in its QE program. "Greek government bonds do not meet the quality criteria required by the ECB," as Paul De Grauwe, a professor of international economics at the London School of Economics, recently wrote.

As De Grauwe goes on to point out, this makes absolutely no sense. Normal investors in the financial markets worry about the quality of a government bond because if they invest in a bad bond, they may lose their money. The ECB can't lose money because it controls the money supply in the eurozone — it can always just print more. There's no technical or economic reason for Greece to be cut out, precisely because the ECB is not just one more investor in the economy. It's pure politics. And cutting Greece out of the QE program has made its economic crisis vastly worse.

There are essentially two parallel systems of possible debt relief for Greece right now. One is the system we hear about in the news: The other eurozone nations get together, pool their revenue, and offer Greece a bailout in exchange for reforms. The latest round in those negotiations was what was decided Wednesday. And while it's inadequate, you can understand why it's so politically contentious: Those other nations can't create more euros on their own, so giving some of their revenue to Greece leaves them worse off, and they're understandably wary.

But the other system is the relationship between the ECB and the eurozone governments. The ECB can create all the euros it wants. So there's no justifiable reason at all for it to cut Greece out of QE or out of a share of the ECB's profits. In fact, there's no reason why the ECB shouldn't just unilaterally buy up all the debt Greece issues, which would allow the Greek government to start running big deficits again and rebuild its economy.

If this second system of debt relief were to actually kick in, it would take an enormous amount of pressure off the first system of debt relief. That in turn would make the political division between Greece, Germany, the IMF, and the rest of them far less poisonous.

That the ECB hasn't done this is raw politics, nothing more.