diff --git a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/complexity.rs b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/complexity.rs
index ccefa6adc4..5544c6825d 100644
--- a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/complexity.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/complexity.rs
@@ -24,7 +24,7 @@ impl fmt::Display for OperationsCount {
         let mut add_plus = "";
         let counts = &self.counts;
         let nb_partitions = counts.nb_partitions();
-        let index = counts.index;
+        let index = &counts.index;
         for src_partition in 0..nb_partitions {
             for dst_partition in 0..nb_partitions {
                 let coeff = counts.values[index.keyswitch_to_small(src_partition, dst_partition)];
@@ -113,4 +113,23 @@ impl Complexity {
         (complexity_cut - actual_complexity) / fks_coeff
     }
 
+    pub fn compressed(self) -> Self {
+        let mut detect_used: Vec<bool> = vec![false; self.counts.len()];
+        for (i, &count) in self.counts.iter().enumerate() {
+            if count > 0.0 {
+                detect_used[i] = true;
+            }
+        }
+        Self {
+            counts: self.counts.compress(&detect_used),
+        }
+    }
+
+    pub fn zero_cost(&self) -> OperationsValue {
+        if self.counts.index.is_compressed() {
+            OperationsValue::zero_compressed(&self.counts.index)
+        } else {
+            OperationsValue::zero(self.counts.nb_partitions())
+        }
+    }
 }
diff --git a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/feasible.rs b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/feasible.rs
index f4786e0e3e..c99108f4e5 100644
--- a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/feasible.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/feasible.rs
@@ -6,6 +6,7 @@ use crate::utils::f64::f64_dot;
 use super::operations_value::OperationsValue;
 use super::partitions::PartitionIndex;
 
+#[derive(Clone)]
 pub struct Feasible {
     // TODO: move kappa here
     pub constraints: Vec<VarianceConstraint>,
@@ -204,4 +205,44 @@ impl Feasible {
             .collect();
         Self::of(&partition_constraints, self.kappa, self.global_p_error)
     }
+
+    pub fn compressed(self) -> Self {
+        let mut detect_used: Vec<bool> = vec![false; self.constraints[0].variance.coeffs.len()];
+        for constraint in &self.constraints {
+            for (i, &coeff) in constraint.variance.coeffs.iter().enumerate() {
+                if coeff > 0.0 {
+                    detect_used[i] = true;
+                }
+            }
+        }
+        let compress = |c: &VarianceConstraint| VarianceConstraint {
+            variance: c.variance.compress(&detect_used),
+            ..(*c)
+        };
+        let constraints = self.constraints.iter().map(compress).collect();
+        let undominated_constraints = self.undominated_constraints.iter().map(compress).collect();
+        Self {
+            constraints,
+            undominated_constraints,
+            ..self
+        }
+    }
+
+    pub fn zero_variance(&self) -> OperationsValue {
+        if self.undominated_constraints[0]
+            .variance
+            .coeffs
+            .index
+            .is_compressed()
+        {
+            OperationsValue::zero_compressed(&self.undominated_constraints[0].variance.coeffs.index)
+        } else {
+            OperationsValue::zero(
+                self.undominated_constraints[0]
+                    .variance
+                    .coeffs
+                    .nb_partitions(),
+            )
+        }
+    }
 }
diff --git a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/operations_value.rs b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/operations_value.rs
index d3a6620a8f..875706aff7 100644
--- a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/operations_value.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/operations_value.rs
@@ -3,7 +3,7 @@ use std::ops::{Deref, DerefMut};
 /**
  * Index actual operations (input, ks, pbs, fks, modulus switching, etc).
  */
-#[derive(Clone, Copy, Debug, Eq, PartialEq, PartialOrd)]
+#[derive(Clone, Debug, Eq, PartialEq, PartialOrd)]
 pub struct Indexing {
     /* Values order
     [
@@ -20,64 +20,111 @@ pub struct Indexing {
     ]
     */
     pub nb_partitions: usize,
+    pub compressed_index: Vec<usize>,
 }
 
-pub const VALUE_INDEX_FRESH: usize = 0;
-pub const VALUE_INDEX_PBS: usize = 1;
-pub const VALUE_INDEX_MODULUS: usize = 2;
+const VALUE_INDEX_FRESH: usize = 0;
+const VALUE_INDEX_PBS: usize = 1;
+const VALUE_INDEX_MODULUS: usize = 2;
 // number of value always present for a partition
-pub const STABLE_NB_VALUES_BY_PARTITION: usize = 3;
+const STABLE_NB_VALUES_BY_PARTITION: usize = 3;
+
+pub const COMPRESSED_0_INDEX: usize = 0; // all 0.0 value are indexed here
+pub const COMPRESSED_FIRST_FREE_INDEX: usize = 1;
 
 impl Indexing {
-    fn nb_keyswitchs_per_partition(self) -> usize {
+    fn uncompressed(nb_partitions: usize) -> Self {
+        Self {
+            nb_partitions,
+            compressed_index: vec![],
+        }
+    }
+
+    fn compress(&self, used: &[bool]) -> Self {
+        assert!(!self.is_compressed());
+        let mut compressed_index = vec![COMPRESSED_0_INDEX; self.nb_coeff()];
+        let mut index = COMPRESSED_FIRST_FREE_INDEX;
+        for (i, &is_used) in used.iter().enumerate() {
+            if is_used {
+                compressed_index[i] = index;
+                index += 1;
+            }
+        }
+        Self {
+            compressed_index,
+            ..(*self)
+        }
+    }
+
+    pub fn is_compressed(&self) -> bool {
+        !self.compressed_index.is_empty()
+    }
+
+    fn nb_keyswitchs_per_partition(&self) -> usize {
         self.nb_partitions
     }
 
-    pub fn nb_coeff_per_partition(self) -> usize {
+    pub fn maybe_compressed(&self, i: usize) -> usize {
+        if self.is_compressed() {
+            self.compressed_index[i]
+        } else {
+            i
+        }
+    }
+
+    pub fn nb_coeff_per_partition(&self) -> usize {
         STABLE_NB_VALUES_BY_PARTITION + 2 * self.nb_partitions
     }
 
-    pub fn nb_coeff(self) -> usize {
+    pub fn nb_coeff(&self) -> usize {
         self.nb_partitions * (STABLE_NB_VALUES_BY_PARTITION + 2 * self.nb_partitions)
     }
 
-    pub fn input(self, partition: usize) -> usize {
+    pub fn input(&self, partition: usize) -> usize {
         assert!(partition < self.nb_partitions);
-        partition * self.nb_coeff_per_partition() + VALUE_INDEX_FRESH
+        self.maybe_compressed(partition * self.nb_coeff_per_partition() + VALUE_INDEX_FRESH)
     }
 
-    pub fn pbs(self, partition: usize) -> usize {
+    pub fn pbs(&self, partition: usize) -> usize {
         assert!(partition < self.nb_partitions);
-        partition * self.nb_coeff_per_partition() + VALUE_INDEX_PBS
+        self.maybe_compressed(partition * self.nb_coeff_per_partition() + VALUE_INDEX_PBS)
     }
 
-    pub fn modulus_switching(self, partition: usize) -> usize {
+    pub fn modulus_switching(&self, partition: usize) -> usize {
         assert!(partition < self.nb_partitions);
-        partition * self.nb_coeff_per_partition() + VALUE_INDEX_MODULUS
+        self.maybe_compressed(partition * self.nb_coeff_per_partition() + VALUE_INDEX_MODULUS)
     }
 
-    pub fn keyswitch_to_small(self, src_partition: usize, dst_partition: usize) -> usize {
+    pub fn keyswitch_to_small(&self, src_partition: usize, dst_partition: usize) -> usize {
         assert!(src_partition < self.nb_partitions);
         assert!(dst_partition < self.nb_partitions);
-        // Skip other partition
-        dst_partition * self.nb_coeff_per_partition()
-        // Skip non keyswitchs
-        + STABLE_NB_VALUES_BY_PARTITION
-        // Select the right keyswicth to small
-        + src_partition
+        self.maybe_compressed(
+            // Skip other partition
+            dst_partition * self.nb_coeff_per_partition()
+            // Skip non keyswitchs
+            + STABLE_NB_VALUES_BY_PARTITION
+            // Select the right keyswicth to small
+            + src_partition,
+        )
     }
 
-    pub fn keyswitch_to_big(self, src_partition: usize, dst_partition: usize) -> usize {
+    pub fn keyswitch_to_big(&self, src_partition: usize, dst_partition: usize) -> usize {
         assert!(src_partition < self.nb_partitions);
         assert!(dst_partition < self.nb_partitions);
-        // Skip other partition
-        dst_partition * self.nb_coeff_per_partition()
-        // Skip non keyswitchs
-        + STABLE_NB_VALUES_BY_PARTITION
-        // Skip keyswitch to small
-        + self.nb_keyswitchs_per_partition()
-        // Select the right keyswicth to big
-        + src_partition
+        self.maybe_compressed(
+            // Skip other partition
+            dst_partition * self.nb_coeff_per_partition()
+            // Skip non keyswitchs
+            + STABLE_NB_VALUES_BY_PARTITION
+            // Skip keyswitch to small
+            + self.nb_keyswitchs_per_partition()
+            // Select the right keyswicth to big
+            + src_partition,
+        )
+    }
+
+    pub fn compressed_size(&self) -> usize {
+        self.compressed_index.iter().copied().max().unwrap_or(0) + 1
     }
 }
 
@@ -92,23 +139,36 @@ pub struct OperationsValue {
 
 impl OperationsValue {
     pub const ZERO: Self = Self {
-        index: Indexing { nb_partitions: 0 },
+        index: Indexing {
+            nb_partitions: 0,
+            compressed_index: vec![],
+        },
         values: vec![],
     };
 
     pub fn zero(nb_partitions: usize) -> Self {
-        let index = Indexing { nb_partitions };
+        let index = Indexing::uncompressed(nb_partitions);
+        let nb_coeff = index.nb_coeff();
         Self {
             index,
-            values: vec![0.0; index.nb_coeff()],
+            values: vec![0.0; nb_coeff],
+        }
+    }
+
+    pub fn zero_compressed(index: &Indexing) -> Self {
+        assert!(index.is_compressed());
+        Self {
+            index: index.clone(),
+            values: vec![0.0; index.compressed_size()],
         }
     }
 
     pub fn nan(nb_partitions: usize) -> Self {
-        let index = Indexing { nb_partitions };
+        let index = Indexing::uncompressed(nb_partitions);
+        let nb_coeff = index.nb_coeff();
         Self {
             index,
-            values: vec![f64::NAN; index.nb_coeff()],
+            values: vec![f64::NAN; nb_coeff],
         }
     }
 
@@ -135,6 +195,32 @@ impl OperationsValue {
     pub fn nb_partitions(&self) -> usize {
         self.index.nb_partitions
     }
+
+    pub fn compress(&self, used: &[bool]) -> Self {
+        self.compress_with(self.index.compress(used))
+    }
+
+    pub fn compress_like(&self, other: Self) -> Self {
+        self.compress_with(other.index)
+    }
+
+    fn compress_with(&self, index: Indexing) -> Self {
+        assert!(!index.compressed_index.is_empty());
+        assert!(self.index.compressed_index.is_empty());
+        let mut values = vec![0.0; index.compressed_size()];
+        for (i, &value) in self.values.iter().enumerate() {
+            #[allow(clippy::option_if_let_else)]
+            let j = index.compressed_index[i];
+            if j == COMPRESSED_0_INDEX {
+                assert!(value == 0.0, "Cannot compress non null value");
+            } else {
+                values[j] = value;
+            }
+        }
+        assert!(values[COMPRESSED_0_INDEX] == 0.0);
+        assert!(!index.compressed_index.is_empty());
+        Self { index, values }
+    }
 }
 
 impl Deref for OperationsValue {
diff --git a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/optimize.rs b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/optimize.rs
index 6c9fbb5957..e46530a8b4 100644
--- a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/optimize.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/optimize.rs
@@ -646,8 +646,8 @@ fn optimize_macro(
 
     let fks_to_optimize = fks_to_optimize(nb_partitions, used_conversion_keyswitch, partition);
     let operations = OperationsCV {
-        variance: OperationsValue::zero(nb_partitions),
-        cost: OperationsValue::zero(nb_partitions),
+        variance: feasible.zero_variance(),
+        cost: complexity.zero_cost(),
     };
     let partition_feasible = feasible.filter_constraints(partition);
 
@@ -907,8 +907,8 @@ pub fn optimize(
 
     let mut caches = persistent_caches.caches();
 
-    let feasible = Feasible::of(&dag.variance_constraints, kappa, None);
-    let complexity = Complexity::of(&dag.operations_count);
+    let feasible = Feasible::of(&dag.variance_constraints, kappa, None).compressed();
+    let complexity = Complexity::of(&dag.operations_count).compressed();
     let used_tlu_keyswitch = used_tlu_keyswitch(&dag);
     let used_conversion_keyswitch = used_conversion_keyswitch(&dag);
 
@@ -1071,8 +1071,8 @@ fn sanity_check(
     );
     let nb_partitions = params.macro_params.len();
     let mut operations = OperationsCV {
-        variance: OperationsValue::zero(nb_partitions),
-        cost: OperationsValue::zero(nb_partitions),
+        variance: feasible.zero_variance(),
+        cost: complexity.zero_cost(),
     };
     let micro_params = &params.micro_params;
     for partition in 0..nb_partitions {
diff --git a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/symbolic_variance.rs b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/symbolic_variance.rs
index 67fc59639d..cdda3b9e19 100644
--- a/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/symbolic_variance.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer/src/optimization/dag/multi_parameters/symbolic_variance.rs
@@ -1,7 +1,7 @@
 use std::fmt;
 
 use crate::optimization::dag::multi_parameters::operations_value::{
-    OperationsValue, VALUE_INDEX_FRESH, VALUE_INDEX_PBS,
+    OperationsValue
 };
 
 /**
@@ -147,9 +147,8 @@ impl SymbolicVariance {
         // this is the maximum value of fresh base noise and pbs base noise
         let mut current_max: f64 = 0.0;
         for partition in 0..self.nb_partitions() {
-            let partition_offset = partition * self.coeffs.index.nb_coeff_per_partition();
-            let fresh_coeff = self.coeffs[partition_offset + VALUE_INDEX_FRESH];
-            let pbs_noise_coeff = self.coeffs[partition_offset + VALUE_INDEX_PBS];
+            let fresh_coeff = self.coeff_input(partition);
+            let pbs_noise_coeff = self.coeff_pbs(partition);
             current_max = current_max.max(fresh_coeff).max(pbs_noise_coeff);
         }
         assert!(1.0 <= current_max);
@@ -177,6 +176,13 @@ impl SymbolicVariance {
         }
         Self { coeffs, ..*self }
     }
+
+    pub fn compress(&self, detect_used: &[bool]) -> Self {
+        Self {
+            coeffs: self.coeffs.compress(detect_used),
+            ..(*self)
+        }
+    }
 }
 
 impl fmt::Display for SymbolicVariance {
diff --git a/compilers/concrete-optimizer/concrete-optimizer/src/utils/f64.rs b/compilers/concrete-optimizer/concrete-optimizer/src/utils/f64.rs
index 91b016ed98..f141fa654f 100644
--- a/compilers/concrete-optimizer/concrete-optimizer/src/utils/f64.rs
+++ b/compilers/concrete-optimizer/concrete-optimizer/src/utils/f64.rs
@@ -3,6 +3,12 @@ pub fn f64_max(values: &[f64], default: f64) -> f64 {
 }
 
 pub fn f64_dot(a: &[f64], b: &[f64]) -> f64 {
+    assert!(
+        a.len() == b.len(),
+        "Dot incompatible size: {} vs {}",
+        a.len(),
+        b.len()
+    );
     let mut sum = 0.0;
     for i in 0..a.len() {
         sum += a[i] * b[i];