Municipal bond investors have been bailing in droves, pulling $4.5 billion from the market last week alone, according to Thomson Reuters.
That's been in large part because of fears of a Fed exit that may not even be applicable to the muni market.
"While municipals have been cheapening in empathy with Treasurys, it is worth noting that this market has never had direct support from the Fed," Citigroup muni analyst George Friedlander said in his weekly update.
"Thus, we believe municipal investors need not worry about a fundamental re-evaluation of the market even after the Fed embarks on its tapering schedule for asset purchases."
Friedlander's best ideas include single-A-rated taxable munis, long-dated high-grade municipals and a switch out of banks (contrary to Lillard's strategy) and industrials into prepay gas and corporate-backed munis.
(Read More: Junk Bonds No Longer Look So Good)
To be sure, though, the road to rate stability is likely to be rocky.
Investors didn't seem to know what to make of Monday's sharp stock market rally that came on the back of an economic reading from the Institute for Supply Management that was better but nothing spectacular.
Until the next round of big data releases pass—the critical nonfarm payrolls report comes Friday—investors should be careful about how much risk they are willing to take on future policy decisions, said George Goncalves, head of U.S. rates strategy at Nomura Securities.
He points out that bond and equity fund flows are about equally positive for the year, indicating that any "Great Rotation" from bonds into stocks has yet to begin.
"The key question on investors' minds is whether the current and much quicker fund outflow ... will continue, or have we moved into a new paradigm where it's the beginning of the end of nonstop bond fund inflows given that the Fed may be taking away its support," he said in a note.
(Read More: Hedge Funds Shift to Stocks, in Time for Pullback)
Goncalves said his portfolio "remains very lean into and out of quarter-end," with plays on a spread widener on the 30-year bond, as well as a steepener between the 10-year note and 30-year inflation breakevens.
He worries that the flow exodus could continue and the Fed might get behind the curve.
"In the grand scheme of things, the total outflow is small compared with the size of the industry, but it's been the pace and reversal of inflow trends that has broader market participants worried," Goncalves said. "We are a bit perplexed why there hasn't been a greater focus on what is happening in the mutual fund space by the Fed."
—By CNBC's Jeff Cox. Follow him @JeffCoxCNBCcom on Twitter.