diff --git a/concrete-optimizer/src/optimization/dag/solo_key/optimize_generic.rs b/concrete-optimizer/src/optimization/dag/solo_key/optimize_generic.rs
index 4e5dcd830..7b4653125 100644
--- a/concrete-optimizer/src/optimization/dag/solo_key/optimize_generic.rs
+++ b/concrete-optimizer/src/optimization/dag/solo_key/optimize_generic.rs
@@ -1,3 +1,5 @@
+use std::ops::RangeInclusive;
+
 use concrete_commons::numeric::UnsignedInteger;
 
 use crate::dag::operator::{Operator, Precision};
@@ -11,6 +13,7 @@ use crate::optimization::wop_atomic_pattern::Solution as WopSolution;
 
 const MINIMAL_WOP_PRECISION: Precision = 9;
 const MAXIMAL_WOP_PRECISION: Precision = 16;
+const WOP_PRECISIONS: RangeInclusive<Precision> = MINIMAL_WOP_PRECISION..=MAXIMAL_WOP_PRECISION;
 
 pub enum Solution {
     WpSolution(WpSolution),
@@ -52,7 +55,26 @@ pub fn optimize<W: UnsignedInteger>(
     default_log_norm2_woppbs: f64,
 ) -> Option<Solution> {
     let max_precision = max_precision(dag);
-    if max_precision < MINIMAL_WOP_PRECISION {
+    let nb_luts = analyze::lut_count_from_dag(dag);
+    let has_luts = nb_luts != 0;
+    if has_luts && WOP_PRECISIONS.contains(&max_precision) {
+        let nb_luts = analyze::lut_count_from_dag(dag);
+        let fallback_16b_precision = 16;
+        let default_log_norm = default_log_norm2_woppbs;
+        let worst_log_norm = analyze::worst_log_norm(dag);
+        let log_norm = default_log_norm.min(worst_log_norm);
+        let opt_sol = wop_optimize::<W>(
+            fallback_16b_precision,
+            security_level,
+            log_norm,
+            maximum_acceptable_error_probability,
+            glwe_log_polynomial_sizes,
+            glwe_dimensions,
+            internal_lwe_dimensions,
+        )
+        .best_solution;
+        opt_sol.map(|sol| Solution::WopSolution(updated_global_p_error(nb_luts, sol)))
+    } else {
         let opt_sol = optimize::optimize::<W>(
             dag,
             security_level,
@@ -63,23 +85,5 @@ pub fn optimize<W: UnsignedInteger>(
         )
         .best_solution;
         opt_sol.map(Solution::WpSolution)
-    } else if max_precision > MAXIMAL_WOP_PRECISION {
-        None
-    } else {
-        let default_log_norm = default_log_norm2_woppbs;
-        let worst_log_norm = analyze::worst_log_norm(dag);
-        let nb_luts = analyze::lut_count_from_dag(dag);
-        let log_norm = default_log_norm.min(worst_log_norm);
-        let opt_sol = wop_optimize::<W>(
-            max_precision as u64,
-            security_level,
-            log_norm,
-            maximum_acceptable_error_probability,
-            glwe_log_polynomial_sizes,
-            glwe_dimensions,
-            internal_lwe_dimensions,
-        )
-        .best_solution;
-        opt_sol.map(|sol| Solution::WopSolution(updated_global_p_error(nb_luts, sol)))
     }
 }