Domestic inflation data due out at 08:00 GMT could spur the rand further if prices rose higher in June than forecast, backing the argument for interest rates to rise further this year.
At 06:47 GMT the rand was at R10.5520 versus the greenback, inching up 0.24% from Tuesday's session close in New York.
Government debt tracked the stronger currency, with yields for the 2026 and 2015 bonds each dipping 3.5 basis points to 8.13% and 6.67% respectively.
Economists polled by Reuters expect CPI to accelerate further above from the central bank's 3% to 6% target band, at 6.7% year-on-year in June.
"Anything above this and the support area of R10.5250 will come under intense pressure by those betting on a more substantial rate increase at the next South African Reserve Bank (sarb) meeting," Standard Bank trader Warrick Butler said.
"If it is a lower print then there may be some urgent questions asked about the Sarb's forecasted inflation trajectory."
The SA Reserve Bank raised the benchmark repo rate for the second time this year last week, citing concerns about upward risks to inflation even as the economy struggles to grow.