On Thursday, the market for multinational mobile networks acted as if the eurozone was about to be swallowed by the Atlantic. Spain-based telecom titan Telefonica (NYSE: TEF) and Italian leader Telecom Italia (NYSE: TI) took it harder than others since their largest markets also happen to be some of the weakest economies on the continent. Both stocks fell more than 6% on Thursday.

But Friday shone a whole new light on the situation. Both Telefonica and Telecom Italia recovered entirely from Thursday's plunge -- and then some.

Spanish prime minister Mariano Rajoy took the stage of his long-planned midyear press meeting to say that he just might consider asking the EU's central bank for a bailout. That's a whole new attitude from the proud Spaniard, and a central cash infusion could breathe new life into the Iberain peninsula's moribund economy. Through trickle-down economics, local phone hero Telefonica would inevitably benefit since approximately one-quarter of its revenue comes from its home country.

Separately, European banking chief Mario Draghi said that the currency union's central bank would focus on short-dated bonds -- giving Spanish and Italian bond rates a breather from inflated prices. The Wall Street Journal explains that exactly the same thing happened to Irish, Greek, and Portuguese bonds just before those troubled nations asked for bailouts.

Telefonica could sure use some good news since rising competition and a grim Spanish economy inspired the company to put its once-mighty dividend on ice. The Italian operator has not taken that drastic step yet, but faces a similarly crummy market while fighting its own government's efforts to increase local competition.

European telecoms that focus on more stable markets saw less of a thrill ride this week. France Telecom (NYSE: FTE) fell no more than 4.6% before climbing to a 2% two-day gain, and British giant Vodafone (NYSE: VOD) largely tuned into the London Olympics and ignored the whole brouhaha.

Besides the paused Telefonica dividend, all of these stocks offer at least 5% yields at today's prices. This could be the perfect time to lock in those generous payout yields since their long-term stability suddenly look much healthier. The world's smartest investors back up the truck to load up on cheap shares when there's blood in the streets, and European telecoms would make sense to those geniuses right now.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.