Redemptions from U.S. bond mutual funds have slowed as investors pulled $3.49 billion during the week of July 14, the smallest weekly withdrawal since the bond-market sell-off in June.

Investors removed $1.03 billion from taxable bond funds and $2.46 billion from those that buy municipal debt in the week ended July 17, according to an statement Wednesday from the Investment Company Institute. Bond funds lost $8.1 billion to withdrawals in the previous week and a record $60 billion in June.

“There will be more travails for bond funds, even if rates stabilize, because returns just won’t be very good,” said Geoff Bobroff, a consultant.

The flight from fixed income began after Federal Reserve Chairman Ben Bernanke told Congress in May that the central bank may start reducing its bond purchases.

Unlimited Digital Access. $1 for 4 weeks.

He told reporters June 19 that policy makers may start decreasing the Fed’s asset purchases later this year and end them by mid-2014 if the economy meets expectations.

Bill Gross’s Pimco Total Return Fund, the world’s largest mutual fund, suffered a record $9.9 billion in net redemptions last month as performance declined amid market losses. It has rebounded since then to beat 96 percent of peers in the past month, helped by falling yields.

The yield on the 10-year Treasury note has dropped to 2.58 percent, from as high as 2.75 percent at the start of July.

The yield was as low as 1.61 percent at the beginning of May. Bonds lose value as rates rise.