diff --git a/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/regen.rs b/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/regen.rs
index 94c9ce3e58..7bca1d69de 100644
--- a/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/regen.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/regen.rs
@@ -1,6 +1,6 @@
 use crate::dag::operator::operator::Operator;
 use crate::dag::operator::OperatorIndex;
-use crate::dag::unparametrized::Dag;
+use crate::dag::unparametrized::{Dag, DagBuilder};
 
 fn reindex_op_inputs(op: &Operator, old_index_to_new: &[usize]) -> Operator {
     let mut op = op.clone();
@@ -20,14 +20,14 @@ fn reindex_op_inputs(op: &Operator, old_index_to_new: &[usize]) -> Operator {
 
 pub(crate) fn regen(
     dag: &Dag,
-    f: &mut dyn FnMut(usize, &Operator, &mut Dag) -> Option<OperatorIndex>,
+    f: &mut dyn FnMut(usize, &Operator, &mut DagBuilder<'_>) -> Option<OperatorIndex>,
 ) -> (Dag, Vec<Vec<OperatorIndex>>) {
     let mut regen_dag = Dag::new();
     let mut old_index_to_new = vec![];
     for (i, op) in dag.operators.iter().enumerate() {
         let op = reindex_op_inputs(op, &old_index_to_new);
         let size = regen_dag.operators.len();
-        if let Some(op_i) = f(i, &op, &mut regen_dag) {
+        if let Some(op_i) = f(i, &op, &mut regen_dag.builder(dag.circuit_tags[i].clone())) {
             old_index_to_new.push(op_i.0);
         } else {
             assert!(size == regen_dag.operators.len());
@@ -37,6 +37,8 @@ pub(crate) fn regen(
             regen_dag.out_shapes.push(dag.out_shapes[i].clone());
             regen_dag.output_tags.push(dag.output_tags[i]);
             regen_dag.circuit_tags.push(dag.circuit_tags[i].clone());
+            op.get_inputs_iter()
+                .for_each(|n| regen_dag.output_tags[n.0].use_as_input());
         }
     }
     (regen_dag, instructions_multi_map(&old_index_to_new))
diff --git a/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/round.rs b/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/round.rs
index c243a33fa1..92b40d85f2 100644
--- a/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/round.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer/src/dag/rewrite/round.rs
@@ -1,9 +1,9 @@
 use crate::dag::operator::{Operator, OperatorIndex};
-use crate::dag::unparametrized::Dag;
+use crate::dag::unparametrized::{Dag, DagBuilder};
 
 use super::regen::regen;
 
-fn regen_round(_: usize, op: &Operator, dag: &mut Dag) -> Option<OperatorIndex> {
+fn regen_round(_: usize, op: &Operator, dag: &mut DagBuilder<'_>) -> Option<OperatorIndex> {
     match *op {
         Operator::Round {
             input,
diff --git a/compilers/concrete-optimizer/concrete-optimizer/src/dag/unparametrized.rs b/compilers/concrete-optimizer/concrete-optimizer/src/dag/unparametrized.rs
index 6c2f3c7e69..54f626ef63 100644
--- a/compilers/concrete-optimizer/concrete-optimizer/src/dag/unparametrized.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer/src/dag/unparametrized.rs
@@ -7,6 +7,24 @@ use std::{collections::HashSet, fmt};
 /// The name of the default. Used when adding operations directly on the dag instead of via a builder.
 const DEFAULT_CIRCUIT: &str = "_";
 
+#[derive(Debug, Clone, PartialEq, Copy)]
+pub(crate) enum OutputKind {
+    // The operator was actively marked as being an output. Using it as input should not turn it into an input.
+    TaggedAsOutput,
+    // The operator was initialized as being an output. Using it as input should turn it into an input.
+    InitializedAsOutput,
+    // The operator was used as input to another operator.
+    UsedAsInput,
+}
+
+impl OutputKind {
+    pub(crate) fn use_as_input(&mut self) {
+        if let OutputKind::InitializedAsOutput = self {
+            *self = OutputKind::UsedAsInput;
+        }
+    }
+}
+
 /// A type referencing every informations related to an operator of the dag.
 #[derive(Debug, Clone)]
 #[allow(unused)]
@@ -16,7 +34,7 @@ pub(crate) struct DagOperator<'dag> {
     pub(crate) operator: &'dag Operator,
     pub(crate) shape: &'dag Shape,
     pub(crate) precision: &'dag Precision,
-    pub(crate) output_tag: &'dag bool,
+    pub(crate) output_tag: &'dag OutputKind,
     pub(crate) circuit_tag: &'dag String,
 }
 
@@ -28,7 +46,10 @@ impl<'dag> DagOperator<'dag> {
 
     /// Returns if the operator is an output.
     pub(crate) fn is_output(&self) -> bool {
-        *self.output_tag
+        match self.output_tag {
+            OutputKind::TaggedAsOutput | OutputKind::InitializedAsOutput => true,
+            OutputKind::UsedAsInput => false,
+        }
     }
 
     /// Returns an iterator over the operators used as input to this operator.
@@ -96,9 +117,9 @@ impl<'dag> DagBuilder<'dag> {
         self.dag.out_shapes.push(self.infer_out_shape(&operator));
         operator
             .get_inputs_iter()
-            .for_each(|id| self.dag.output_tags[id.0] = false);
+            .for_each(|id| self.dag.output_tags[id.0].use_as_input());
         self.dag.operators.push(operator);
-        self.dag.output_tags.push(true);
+        self.dag.output_tags.push(OutputKind::InitializedAsOutput);
         self.dag.circuit_tags.push(self.circuit.clone());
         OperatorIndex(i)
     }
@@ -296,7 +317,7 @@ impl<'dag> DagBuilder<'dag> {
     pub fn tag_operator_as_output(&mut self, operator: OperatorIndex) {
         assert!(operator.0 < self.dag.len());
         debug_assert!(self.dag.circuit_tags[operator.0] == self.circuit);
-        self.dag.output_tags[operator.0] = true;
+        self.dag.output_tags[operator.0] = OutputKind::TaggedAsOutput;
     }
 
     pub fn get_circuit(&self) -> DagCircuit<'_> {
@@ -373,7 +394,7 @@ pub struct Dag {
     // Collect all operators output precision
     pub(crate) out_precisions: Vec<Precision>,
     // Collect whether operators are tagged as outputs
-    pub(crate) output_tags: Vec<bool>,
+    pub(crate) output_tags: Vec<OutputKind>,
     // Collect the circuit the operators are associated with
     pub(crate) circuit_tags: Vec<String>,
 }
@@ -633,7 +654,7 @@ impl Dag {
     /// tagged using this method.
     pub fn tag_operator_as_output(&mut self, operator: OperatorIndex) {
         assert!(operator.0 < self.len());
-        self.output_tags[operator.0] = true;
+        self.output_tags[operator.0] = OutputKind::TaggedAsOutput;
     }
 
     /// Returns the number of circuits in the dag.
@@ -647,6 +668,18 @@ mod tests {
     use super::*;
     use crate::dag::operator::Shape;
 
+    #[test]
+    fn output_marking() {
+        let mut graph = Dag::new();
+        let mut builder = graph.builder("main1");
+        let a = builder.add_input(1, Shape::number());
+        let b = builder.add_input(1, Shape::number());
+        builder.tag_operator_as_output(b);
+        let _ = builder.add_dot([a, b], [1, 1]);
+        assert!(graph.get_operator(b).is_output());
+        assert!(!graph.get_operator(a).is_output());
+    }
+
     #[test]
     #[allow(clippy::many_single_char_names)]
     fn graph_builder() {