The weakness of high-yield stock funds is “a value-versus-growth thing,” said Jeff Porter, chief investment officer at Sullivan Bruyette Speros & Blayney, a financial advice firm. “Value stocks have underperformed, and with interest rates so low, growth companies’ earnings way out in the future are more highly valued today.”

Because of the strong demand for stocks in companies that display stable growth, and in other high-yield niches like utilities, funds that pay high income have become expensive, with many trading at a premium to the broad stock market, even though they have underperformed, Mr. Porter said.

“As people have chased utilities and consumer staples, that desire for safety has bid those up to prices that are no longer adding value,” he said.

Mr. Porter, like Ms. Pai, prefers companies that are likely to increase their dividends, even if their current yields are not that high. A recent report by Bank of America noted that stocks with sustainable or growing yields are trading at a rare valuation discount to high-yield stocks. That could provide a cushion should rates fall.

And, of course, the Federal Reserve may keep tightening monetary policy, or maybe just signal that it’s not going to be as accommodative as Wall Street anticipates. The central bank did an about-face in January, shifting abruptly from hawkish to dovish, that sent stocks soaring in January and February, and reaffirmed its stance on March 20; a reversal is not out of the question. Bank of America forecasts that the Fed will raise rates later this year, and its strategists recommend “dividend growth stocks with some cyclicality that can raise payout ratios as rates rise.”

The search for yield can be so difficult that Gregg Fisher, head of research at Gerstein Fisher Funds, recommends calling it off, or at least relegating it to a minor role when building a portfolio, even one intended to generate income. He encourages investors to focus on the best businesses, regardless of their dividend profiles. They ultimately will be most rewarding to shareholders, whether they receive dividend payments or sell appreciated stock.

“A dividend portfolio is less diversified and concentrated in fewer sectors,” he said. “If the goal is to produce cash flow, not accounting income, you should own a diversified portfolio that has some dividend payers and other stocks that don’t pay dividends at all. You end up with more cash flow and better results overall.”