diff --git a/frontends/concrete-python/concrete/fhe/mlir/processors/assign_bit_widths.py b/frontends/concrete-python/concrete/fhe/mlir/processors/assign_bit_widths.py
index 644cafe5c8..ef8863e02b 100644
--- a/frontends/concrete-python/concrete/fhe/mlir/processors/assign_bit_widths.py
+++ b/frontends/concrete-python/concrete/fhe/mlir/processors/assign_bit_widths.py
@@ -43,13 +43,13 @@ def __init__(
         self.shifts_with_promotion = shifts_with_promotion
 
     def apply(self, graph: Graph):
-        optimizer = z3.Optimize()
+        solver = z3.Solver()
 
         max_bit_width: z3.Int = z3.Int("max")
         bit_widths: Dict[Node, z3.Int] = {}
 
         additional_constraints = AdditionalConstraints(
-            optimizer,
+            solver,
             graph,
             bit_widths,
             self.comparison_strategy_preference,
@@ -69,19 +69,17 @@ def apply(self, graph: Graph):
             bit_width = z3.Int(f"%{i}")
             bit_widths[node] = bit_width
 
-            optimizer.add(max_bit_width >= bit_width)
-            optimizer.add(bit_width >= required_bit_width)
+            solver.add(max_bit_width >= bit_width)
+            solver.add(bit_width >= required_bit_width)
 
             additional_constraints.generate_for(node, bit_width)
 
         if self.single_precision:
             for bit_width in bit_widths.values():
-                optimizer.add(bit_width == max_bit_width)
+                solver.add(bit_width == max_bit_width)
 
-        optimizer.minimize(sum(bit_width**2 for bit_width in bit_widths.values()))
-
-        assert optimizer.check() == z3.sat
-        model = optimizer.model()
+        assert solver.check() == z3.sat
+        model = solver.model()
 
         for node, bit_width in bit_widths.items():
             assert isinstance(node.output.dtype, Integer)
@@ -99,7 +97,7 @@ class AdditionalConstraints:
     AdditionalConstraints class to customize bit-width assignment step easily.
     """
 
-    optimizer: z3.Optimize
+    solver: z3.Solver
     graph: Graph
     bit_widths: Dict[Node, z3.Int]
 
@@ -114,14 +112,14 @@ class AdditionalConstraints:
 
     def __init__(
         self,
-        optimizer: z3.Optimize,
+        solver: z3.Solver,
         graph: Graph,
         bit_widths: Dict[Node, z3.Int],
         comparison_strategy_preference: List[ComparisonStrategy],
         bitwise_strategy_preference: List[BitwiseStrategy],
         shifts_with_promotion: bool,
     ):
-        self.optimizer = optimizer
+        self.solver = solver
         self.graph = graph
         self.bit_widths = bit_widths
 
@@ -192,12 +190,12 @@ def has_overflow_protection(self, node: Node, preds: List[Node]) -> bool:
 
     def inputs_share_precision(self, node: Node, preds: List[Node]):
         for i in range(len(preds) - 1):
-            self.optimizer.add(self.bit_widths[preds[i]] == self.bit_widths[preds[i + 1]])
+            self.solver.add(self.bit_widths[preds[i]] == self.bit_widths[preds[i + 1]])
 
     def inputs_and_output_share_precision(self, node: Node, preds: List[Node]):
         self.inputs_share_precision(node, preds)
         if len(preds) != 0:
-            self.optimizer.add(self.bit_widths[preds[-1]] == self.bit_widths[node])
+            self.solver.add(self.bit_widths[preds[-1]] == self.bit_widths[node])
 
     def inputs_require_one_more_bit(self, node: Node, preds: List[Node]):
         for pred in preds:
@@ -206,7 +204,7 @@ def inputs_require_one_more_bit(self, node: Node, preds: List[Node]):
             actual_bit_width = pred.output.dtype.bit_width
             required_bit_width = actual_bit_width + 1
 
-            self.optimizer.add(self.bit_widths[pred] >= required_bit_width)
+            self.solver.add(self.bit_widths[pred] >= required_bit_width)
 
     def comparison(self, node: Node, preds: List[Node]):
         assert len(preds) == 2
@@ -226,11 +224,11 @@ def comparison(self, node: Node, preds: List[Node]):
         for strategy in strategies + fallback:
             if strategy.can_be_used(x.output, y.output):
                 new_x_bit_width, new_y_bit_width = strategy.promotions(x.output, y.output)
-                self.optimizer.add(self.bit_widths[x] >= new_x_bit_width)
-                self.optimizer.add(self.bit_widths[y] >= new_y_bit_width)
+                self.solver.add(self.bit_widths[x] >= new_x_bit_width)
+                self.solver.add(self.bit_widths[y] >= new_y_bit_width)
 
                 if strategy == ComparisonStrategy.ONE_TLU_PROMOTED:
-                    self.optimizer.add(self.bit_widths[x] == self.bit_widths[y])
+                    self.solver.add(self.bit_widths[x] == self.bit_widths[y])
 
                 node.properties["strategy"] = strategy
                 break
@@ -252,11 +250,11 @@ def bitwise(self, node: Node, preds: List[Node]):
         for strategy in strategies + fallback:
             if strategy.can_be_used(x.output, y.output):
                 new_x_bit_width, new_y_bit_width = strategy.promotions(x.output, y.output)
-                self.optimizer.add(self.bit_widths[x] >= new_x_bit_width)
-                self.optimizer.add(self.bit_widths[y] >= new_y_bit_width)
+                self.solver.add(self.bit_widths[x] >= new_x_bit_width)
+                self.solver.add(self.bit_widths[y] >= new_y_bit_width)
 
                 if strategy == BitwiseStrategy.ONE_TLU_PROMOTED:
-                    self.optimizer.add(self.bit_widths[x] == self.bit_widths[y])
+                    self.solver.add(self.bit_widths[x] == self.bit_widths[y])
 
                 node.properties["strategy"] = strategy
                 break
@@ -266,7 +264,7 @@ def bitwise(self, node: Node, preds: List[Node]):
             and node.properties["strategy"] == BitwiseStrategy.CHUNKED
             and self.shifts_with_promotion
         ):
-            self.optimizer.add(self.bit_widths[x] == self.bit_widths[node])
+            self.solver.add(self.bit_widths[x] == self.bit_widths[node])
 
     # ==========
     # Operations