The rand was up 0.6 percent at 8.09 to the dollar by 0640 GMT, compared to an 8.1550 close in the New York market on Monday. The unit is approaching its 100-day exponential moving average, having blasted through the 50-day average - another important level - at the end of last week.
After that, charts suggest the currency will be looking at 8.05.
"Given the rand's support at 8.20 a breach of 8.05 would signal that the rand bulls are finding further traction," said Judy Padayachee, a technical strategist at Absa Capital.
"My previous recommendation had been to short the rand at 8.20 but if the rand goes below 8.05 then that short recommendation is no longer in place. Such a breakout would then open up the 7.70 level."
Dealers say more positive news out of the euro region would be needed to push the rand through the psychologically key 8 rand level.
Yields on government paper were down, with the 2021 issue at 7.205 percent, approaching a lifetime low of 7.128 percent hit in December 2008 as foreigners piled into South Africa's relatively high-yielding debt.
Last month, buying by offshore accounts saw the second biggest monthly inflow into the local debt market.
The benchmark three-year bond was at 5.99 percent, not too far from its record 5.97 hit last month while the yield on the 14-year issue hit a near 10-month low.
Government will sell two new bonds, the 2023 and 2048 along with the 2026 paper at auction later in the session. The results are due after the sale closes at 0900 GMT.
The market will be watching for car sales data at 0900 GMT to see how much discretionary spending took place in June as consumers tightened purse strings with the economy showing signs of slowing.?AFP