LONDON -- Like every wise Fool, I love buying top-quality stocks at lowly valuations. The last couple of years have been a great time to be an investor, because there have been plenty of opportunities around.

Here are three stocks I bought on bad news whose futures are looking brighter.

Viva Aviva!
I had a couple of bites at struggling insurance giant Aviva (LSE:AV) in spring and summer 2010, buying at 370 pence and 314 pence -- roughly half its pre-banking-crisis valuation. Aviva has been hit by its hefty exposure to stricken Europe, where it does 60% of its business. That slam-dunked its share price to about seven times earnings and left it yielding a whopping 9%. No savings account has ever paid me that, and I don't expect it ever will. I suspected things would get worse before they got better, and they did. Last May, a shareholder revolt dispatched chief executive Andrew Moss to the scaffold. I wasn't up in arms, because I was in for the long haul, and I was still getting that dividend.

Aviva has been busily offloading its noncore segments and playing catch up in Asia-Pacific, where it trails Prudential and Legal & General. I don't expect to see the benefit of this for a few years, but the stock has benefited from the recent market upturn, its share price leaping 40% from last July's low of 2.64 pounds to around 3.70 pounds. I'm up 7%, and Aviva still looks cheap, on a price-to-earnings ratio of just 8 times earnings, roughly half the FTSE 100 average, and a yield of 7%. After three years of negative earnings-per-share growth, the consensus forecast is a whopping 117% for 2013. I was glad to see UBS recently praise Aviva's "turnaround" and rate it a "buy." I've bought, I'm holding, and I'm happy.

Mine's a miner
As fears over global growth intensified last summer, the mining sector took quite a knock. As I was underexposed to this sector, I decided it was a good time to buy diversified mining giant BHP Billiton (LSE:BLT) in August 2012 at 19.40 pounds. I am now up a modest 7%, thanks to QE3 and the recent upswing in sentiment. That isn't enough to retire on, but it does give me a cushion for the next bout of market bumpiness. That's what I like about buying stocks when they're struggling: A spot of good news quickly lifts you into positive territory. There was more good news this week, with BHP Billiton's half-year production report predicting compound annual growth of 10% in copper equivalent terms over the next two years. Deutsche Bank rates it a "buy," lifting its target price 10 pence to 23.25 pounds. For me, this is a long-term hold. There may be trouble in China ahead, but as I'm investing for 10 to 20 years, so what? I am also pocketing a pleasant 3.3% yield. Buy cheap, hold long -- what's not to like?

One hip stock
Remember how troubled stock markets were in autumn 2011? While investors panicked, The Motley Fool was coolly telling anybody who would listen that it was a great time to buy shares. Happily, I was listening. So what made me choose surgical-appliance specialists Smith & Nephew (LSE:SN)? Partly the fact that my parents proudly boast two plastic hips and one plastic knee between them. As we all get older and live longer, more and more of us will need our worn-out parts replaced. This FTSE 100-listed orthopedic prosthesis maker looked like a great way to invest in the aging global population. I bought in November 2011 at 5.49 pounds, and I'm already up more than 30%, with the stock trading at 7.28 pounds. Smith & Nephew now looks fully valued at 15.8 times earnings -- roughly in line with the FTSE 100. It yields a measly 1.5%, covered a whopping 4.3 times, but there is talk of a big hike on the way. It is a good, solid company, with projected EPS growth of 6% this year and 9% in 2014. I'm not expecting it to go on a sudden charge, but like my parents, it should remain sprightly for some time yet.

Five more to think about
I'm not talking 10-baggers here -- just good, solid stocks bought at bargain prices. I expect plenty more growth to come when the global economy finally starts motoring.

If you're on the hunt for similar stock opportunities, you might find them in our special in-depth report: "Eight Top Blue Chips Held By Britain's Super Investor." This report by Motley Fool analysts is completely free and shows where Invesco-Perpetual's dividend dazzler Neil Woodford believes the best high-yield stocks are to be found today. Availability of this report is strictly limited, so please download it now.

Harvey owns Aviva, Prudential, BHP Billiton, and Smith & Nephew. The Motley Fool owns shares in Smith & Nephew. The Motley Fool has a disclosure policy. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. Try any of our Foolish newsletter services free for 30 days.