CHRISTINE LAGARDE, the IMF's managing director, boasted of a “Washington moment”. At its spring meetings in the American capital this month, the fund saw its lending power almost double, thanks to the promise of $430 billion in loans from more than a score of its members. The official goal is to boost a “global firewall” against crisis. The unofficial hope is that a fatter IMF will help ease fears about the euro, by bolstering the €700 billion ($925 billion) that euro-zone economies have pledged in their own rescue funds.

Europeans often simply add the two numbers together, implying there is now a vast $1.4 trillion stash. Not so. Look behind the fat figures and you find a lot of fuzzy maths and wishful thinking—just as worsening news in Spain brings talk of that country needing a rescue (see article).

Start with the IMF. Assuming countries make good on their pledges, the money itself is real. The biggest collective contribution will come from the euro-zone countries, which have promised to lend the fund $200 billion between them. Japan is the biggest single donor, with a $60 billion pledge motivated partly by a desire not to be eclipsed by China, partly by fears about its own economic vulnerability. Big emerging economies, such as China, Russia and Brazil, agreed to chip in. Their contribution, and that of others such as Britain, will be contingent on reforms to the fund's governance, which reduce Europe's clout and increase that of emerging economies. (America, notably, did not contribute.)

Barring a big fight over its governance, the fund should be flusher soon. But no one wants to write a blank cheque for the rich euro zone. Canada (which itself did not contribute) called for a double lock: future IMF lending to the euro zone would need to be approved by a vote among non-European members. That probably will not happen, but the fund, at best, will be a minority contributor to future rescues.

So the big bucks will have to come from Europe's own rescue funds. And they are scantier than they seem. Both the EFSF (the existing rescue facility) and the ESM (a new permanent fund) need to raise resources by issuing debt. The EFSF backs its bonds with guarantees from the dwindling number of AAA-rated governments; the ESM will have some paid-in capital. But both could find it hard to raise the large sums that might be required for, say, a swift bank recapitalisation in Spain.

So speculation is growing that the funds would not bother with hard cash. One idea is for Spain to have a system-wide asset-protection scheme, where the banks' toxic assets would be insured by euro-zone guarantees. Another is for the rescue funds to issue bonds to Spain's own bank-rescue fund, just as the EFSF gave Greek bondholders a bond instead of cash as part of that country's debt restructuring.

Explore our interactive guide to Europe's troubled economies

Another problem is that both the IMF and ESM are considered “preferred creditors”, which means any borrowing from them is first in line for repayment. If rescue money is sent to the Spanish government to prop up its banks, those same banks' holdings of government bonds may be worth less. A big rescue could actually end up reducing confidence. The newly thickened firewall is less solid than it appears.