diff --git a/crates/whir/src/dft.rs b/crates/whir/src/dft.rs
index 277597eb8..8f2901c2e 100644
--- a/crates/whir/src/dft.rs
+++ b/crates/whir/src/dft.rs
@@ -62,13 +62,38 @@ impl<F: TwoAdicField> EvalsDft<F> {
     }
 
     pub(crate) fn update_twiddles(&self, fft_len: usize) {
-        // TODO: This recomputes the entire table from scratch if we
-        // need it to be larger, which is wasteful.
         let mut guard = self.twiddles.write().unwrap();
-        let curr_max_fft_len = 1 << guard.len();
-        if fft_len > curr_max_fft_len {
+
+        let lg_n = log2_strict_usize(fft_len);
+
+        //if the current size is already big enough we don't do anything
+        if lg_n <= guard.len() {
+            return;
+        }
+
+        //if current twiddles is empty we compute from nothing
+        if guard.is_empty() {
             *guard = self.roots_of_unity_table(fft_len);
+            return;
         }
+
+        let diff_log = lg_n - guard.len();
+        let nb_steps = 1 << diff_log; //number of missing points between each preexisting points
+
+        let generator = F::two_adic_generator(lg_n);
+
+        let table = guard[0].clone();
+        let mut nth_root = Vec::with_capacity(table.len() * nb_steps);
+        for &base in &table {
+            nth_root.extend(generator.shifted_powers(base).take(nb_steps));
+        }
+
+        let old_twiddles = std::mem::take(&mut *guard);
+        let mut twiddles = Vec::with_capacity(diff_log + old_twiddles.len());
+        twiddles.extend((0..diff_log).map(|i| nth_root.iter().step_by(1 << i).copied().collect::<Vec<_>>()));
+        twiddles.extend(old_twiddles);
+
+        *guard = twiddles;
     }
 }