We study the $δ$-discretized sum-product estimates for well spaced sets. Our main result is: for a fixed $α\in(1,\frac{3}{2}]$, we prove that for any $\sim|A|^{-1}$-separated set $A\subset[1,2]$ and $δ=|A|^{-α}$, we have: $\mathcal{N}(A+A, δ)\cdot \mathcal{N}(AA, δ) \gtrsim_ε|A|δ^{-1+ε}$.