diff --git a/kerngen/pisa_generators/ntt.py b/kerngen/pisa_generators/ntt.py
index 383041dc..316de6cc 100644
--- a/kerngen/pisa_generators/ntt.py
+++ b/kerngen/pisa_generators/ntt.py
@@ -36,25 +36,21 @@ def butterflies_ops(
     """Helper to return butterflies pisa operations for NTT/INTT"""
     ntt_stages_div_by_two = context.ntt_stages % 2
 
+    # generate the stages, which depends on the total ntt stages.
+    stage_dst_srcs = [
+        (
+            (stage, outtmp, output)
+            if ntt_stages_div_by_two == stage % 2
+            else (stage, output, outtmp)
+        )
+        for stage in range(context.ntt_stages)
+    ]
+
+    # For INTTs, start with input0 on the first stage destinations
     if init_input is True:
-        # intt
-        stage_dst_srcs = [
-            (
-                (stage, outtmp, output)
-                if ntt_stages_div_by_two == stage % 2
-                else (stage, output, outtmp)
-            )
-            for stage in range(context.ntt_stages)
-        ]
         stage_dst_srcs[0] = (
             (0, outtmp, input0) if ntt_stages_div_by_two == 0 else (0, output, input0)
         )
-    else:
-        # ntt
-        stage_dst_srcs = [
-            ((stage, outtmp, output) if stage % 2 == 0 else (stage, output, outtmp))
-            for stage in range(context.ntt_stages)
-        ]
 
     return [
         op(
@@ -94,15 +90,21 @@ def to_pisa(self) -> list[PIsaOp]:
         # TODO We need to decide whether output symbols need to be defined
         outtmp = Polys("outtmp", self.output.parts, self.output.rns)
 
-        # Essentially a scalar mul since psi 1 part
-        mul = Mul(self.context, self.output, self.input0, psi)
+        # control the input for the butterfly method.
+        if self.context.ntt_stages % 2 == 0:
+            # Essentially a scalar mul since psi 1 part
+            mul = Mul(self.context, self.output, self.input0, psi)
+            butterfly_input = outtmp
+        else:
+            mul = Mul(self.context, outtmp, self.input0, psi)
+            butterfly_input = self.input0
 
         butterflies = butterflies_ops(
             pisa_op.NTT,
             context=self.context,
             output=self.output,
             outtmp=outtmp,
-            input0=self.input0,
+            input0=butterfly_input,
         )
 
         return mixed_to_pisa_ops(mul, butterflies)