diff --git a/src/centralized_telescope/params.rs b/src/centralized_telescope/params.rs
index fa0f6cf6..806428c8 100644
--- a/src/centralized_telescope/params.rs
+++ b/src/centralized_telescope/params.rs
@@ -16,132 +16,239 @@ pub struct Params {
     pub dfs_bound: u64,
 }
 
-impl Params {
-    /// Setup algorithm taking as input the security parameters, the set size
-    /// and the lower bound and returning the internal parameters Params
-    pub(super) fn new(
-        soundness_param: f64,
-        completeness_param: f64,
-        set_size: u64,
-        lower_bound: u64,
-    ) -> Self {
-        let set_size_f64 = set_size as f64;
-        let lower_bound_f64 = lower_bound as f64;
+pub(super) struct Small {
+    completeness_param: f64,
+}
 
-        let proof_size_f64 = {
-            let numerator = soundness_param + completeness_param.log2() + 5.0 - LOG2_E.log2();
-            let denominator = (set_size_f64 / lower_bound_f64).log2();
-            (numerator / denominator).ceil()
-        };
+pub(super) struct Mid {
+    completeness_param: f64,
+    completeness_param1: f64,
+    set_size: u64,
+}
+
+pub(super) struct High {
+    completeness_param: f64,
+    completeness_param2: f64,
+}
+
+pub(super) enum Cases {
+    Small,
+    Mid,
+    High,
+}
+
+/// Trait to compute internal parameters depending on which case we are
+pub(super) trait Case {
+    /// Trait constructor
+    fn new(completeness_param: f64, set_size: u64, proof_size: f64) -> Self;
+
+    /// Returns the maximum number of retries
+    fn max_retries(&self) -> u64;
+
+    /// Returns the search width
+    fn search_width(&self, proof_size: f64) -> u64;
+
+    /// Returns the valid proof probability
+    fn valid_proof_probability(&self, search_width: u64) -> f64;
+
+    /// Returns the DFS bound
+    fn dfs_bound(&self, proof_size: f64, search_width: u64) -> u64;
+
+    /// Returns Params
+    fn create_params(&self, proof_size: f64) -> Params {
+        let search_width = self.search_width(proof_size);
+        Params {
+            proof_size: proof_size as u64,
+            max_retries: self.max_retries(),
+            search_width,
+            valid_proof_probability: self.valid_proof_probability(search_width),
+            dfs_bound: self.dfs_bound(proof_size, search_width),
+        }
+    }
+}
 
+impl Cases {
+    pub(super) fn which(completeness_param: f64, set_size: u64, proof_size: u64) -> Cases {
+        let set_size_f64 = set_size as f64;
+        let proof_size_f64 = proof_size as f64;
         let ratio = 9.0 * set_size_f64 * LOG2_E / ((17.0 * proof_size_f64).powi(2));
         let s1 = ratio - 7.0;
         let s2 = ratio - 2.0;
 
         if s1 < 1.0 || s2 < 1.0 {
             // Small case, i.e. set_size <= λ^2
-            Params::param_small_case(completeness_param, proof_size_f64)
+            Cases::Small
         } else {
             let completeness_param2 = completeness_param.min(s2);
             if proof_size_f64 < completeness_param2 {
                 // Case 3, Theorem 14, i.e.  set_size >= λ^3
-                Params::param_high_case(
-                    completeness_param,
-                    set_size,
-                    proof_size_f64,
-                    completeness_param2,
-                )
+                Cases::High
             } else {
                 // Case 2, Theorem 13, i.e. λ^2 < set_size < λ^3
-                Params::param_mid_case(completeness_param, set_size, proof_size_f64, s1)
+                Cases::Mid
             }
         }
     }
+}
 
-    /// Helper function that returns Params, used when set_size <= λ^2
-    fn param_small_case(completeness_param: f64, proof_size_f64: f64) -> Params {
-        let ln12 = (12f64).ln();
-        let search_width = (32.0 * ln12 * proof_size_f64).ceil();
-        Params {
-            proof_size: proof_size_f64 as u64,
-            max_retries: completeness_param as u64,
-            search_width: search_width as u64,
-            valid_proof_probability: 2.0 * ln12 / search_width,
-            dfs_bound: (8.0 * (proof_size_f64 + 1.0) * search_width / ln12).floor() as u64,
-        }
+impl Case for Small {
+    fn new(completeness_param: f64, _set_size: u64, _proof_size: f64) -> Self {
+        Self { completeness_param }
     }
 
-    /// Helper function that returns Params, used when set_size >= λ^3
-    fn param_high_case(
-        completeness_param: f64,
-        set_size: u64,
-        proof_size_f64: f64,
-        completeness_param2: f64,
-    ) -> Params {
-        let l2 = completeness_param2 + 2.0;
-        let search_width = (16.0 * proof_size_f64 * l2 / LOG2_E).ceil();
-        debug_assert!(set_size as f64 >= search_width * search_width * LOG2_E / (9.0 * l2));
-        Params {
-            proof_size: proof_size_f64 as u64,
-            max_retries: (completeness_param / completeness_param2).ceil() as u64,
-            search_width: search_width as u64,
-            valid_proof_probability: 2.0 * l2 / (search_width * LOG2_E),
-            dfs_bound: (((l2 + proof_size_f64.log2()) / l2)
-                * (3.0 * proof_size_f64 * search_width / 4.0)
-                + search_width
-                + proof_size_f64)
-                .floor() as u64,
+    fn max_retries(&self) -> u64 {
+        self.completeness_param as u64
+    }
+
+    fn search_width(&self, proof_size: f64) -> u64 {
+        (32.0 * (12f64).ln() * proof_size).ceil() as u64
+    }
+
+    fn valid_proof_probability(&self, search_width: u64) -> f64 {
+        2.0 * 12f64.ln() / search_width as f64
+    }
+
+    fn dfs_bound(&self, proof_size: f64, search_width: u64) -> u64 {
+        (8.0 * (proof_size + 1.0) * search_width as f64 / (12f64).ln()).ceil() as u64
+    }
+}
+
+impl Case for High {
+    fn new(completeness_param: f64, set_size: u64, proof_size: f64) -> Self {
+        let ratio = 9.0 * set_size as f64 * LOG2_E / ((17.0 * proof_size).powi(2));
+        let s2 = ratio - 2.0;
+        let completeness_param2 = completeness_param.min(s2);
+
+        Self {
+            completeness_param,
+            completeness_param2,
         }
     }
 
-    /// Helper function that returns Params, used when λ^2 < set_size < λ^3
-    fn param_mid_case(
-        completeness_param: f64,
-        set_size: u64,
-        proof_size_f64: f64,
-        s1: f64,
-    ) -> Params {
-        fn max_vertices_visited(proof_size: f64, l1: f64) -> f64 {
-            fn factorial_check(max_v: f64, l1: f64) -> bool {
-                let bound = (-l1).exp2();
-                let mut factor = (max_v.ceil() as u64).saturating_add(1);
-                let max_v_2 = max_v + 2.0;
-                let exp_1_over_max_v = max_v.recip().exp();
-                let mut ratio = (14.0 * max_v * max_v * max_v_2 * exp_1_over_max_v)
-                    / (max_v_2 - exp_1_over_max_v);
-                while factor != 0 {
-                    ratio /= factor as f64;
-                    if ratio <= bound {
-                        return true;
-                    }
-                    factor = factor.saturating_sub(1);
+    fn max_retries(&self) -> u64 {
+        (self.completeness_param / self.completeness_param2).ceil() as u64
+    }
+
+    fn search_width(&self, proof_size: f64) -> u64 {
+        (16.0 * proof_size * (self.completeness_param2 + 2.0) / LOG2_E).ceil() as u64
+    }
+
+    fn valid_proof_probability(&self, search_width: u64) -> f64 {
+        (4.0 + 2.0 * self.completeness_param2) / (search_width as f64 * LOG2_E)
+    }
+
+    fn dfs_bound(&self, proof_size: f64, search_width: u64) -> u64 {
+        let search_width_f64 = search_width as f64;
+        ((1.0 + proof_size.log2() * (self.completeness_param2 + 2.0).recip())
+            * 3.0
+            * proof_size
+            * search_width_f64
+            / 4.0
+            + proof_size
+            + search_width_f64)
+            .floor() as u64
+    }
+}
+
+impl Mid {
+    fn max_vertices_visited(proof_size: f64, l1: f64) -> f64 {
+        fn factorial_check(max_v: f64, l1: f64) -> bool {
+            let bound = (-l1).exp2();
+            let mut factor = (max_v.ceil() as u64).saturating_add(1);
+            let max_v_2 = max_v + 2.0;
+            let exp_1_over_max_v = max_v.recip().exp();
+            let mut ratio =
+                (14.0 * max_v * max_v * max_v_2 * exp_1_over_max_v) / (max_v_2 - exp_1_over_max_v);
+            while factor != 0 {
+                ratio /= factor as f64;
+                if ratio <= bound {
+                    return true;
                 }
-                false
+                factor = factor.saturating_sub(1);
             }
-            let mut max_v = proof_size;
-            while !factorial_check(max_v, l1) {
-                max_v += 1.0;
-            }
-            max_v
+            false
+        }
+        let mut max_v = proof_size;
+        while !factorial_check(max_v, l1) {
+            max_v += 1.0;
         }
+        max_v
+    }
+}
+
+impl Case for Mid {
+    fn new(completeness_param: f64, set_size: u64, proof_size: f64) -> Self {
+        let ratio = 9.0 * set_size as f64 * LOG2_E / ((17.0 * proof_size).powi(2));
+        let s1 = ratio - 7.0;
         let completeness_param1 = completeness_param.min(s1);
-        let lbar = (completeness_param1 + 7.0) / LOG2_E;
-        let search_width = (16.0 * proof_size_f64 * lbar).ceil();
-        let lbar_over_sw = lbar / search_width;
-        debug_assert!(set_size as f64 >= search_width * search_width / (9.0 * lbar));
-
-        let max_v = max_vertices_visited(proof_size_f64, completeness_param1);
-        let exponential = (2.0 * proof_size_f64 * max_v * lbar / set_size as f64
-            + 7.0 * proof_size_f64 / max_v)
+
+        Self {
+            completeness_param,
+            completeness_param1,
+            set_size,
+        }
+    }
+
+    fn max_retries(&self) -> u64 {
+        (self.completeness_param / self.completeness_param1).ceil() as u64
+    }
+
+    fn search_width(&self, proof_size: f64) -> u64 {
+        (16.0 * proof_size * (self.completeness_param1 + 7.0) / LOG2_E).ceil() as u64
+    }
+
+    fn valid_proof_probability(&self, search_width: u64) -> f64 {
+        2.0 * (self.completeness_param1 + 7.0) / (LOG2_E * search_width as f64)
+    }
+
+    fn dfs_bound(&self, proof_size: f64, search_width: u64) -> u64 {
+        let search_width_f64 = search_width as f64;
+        let lbar = (self.completeness_param1 + 7.0) / LOG2_E;
+        let max_v = Mid::max_vertices_visited(proof_size, self.completeness_param1);
+        let exponential = (2.0 * proof_size * max_v * lbar / self.set_size as f64
+            + 7.0 * proof_size / max_v)
             .exp();
-        Params {
-            proof_size: proof_size_f64 as u64,
-            max_retries: (completeness_param / completeness_param1).ceil() as u64,
-            search_width: search_width as u64,
-            valid_proof_probability: 2.0 * lbar_over_sw,
-            dfs_bound: ((max_v * lbar_over_sw + 1.0) * exponential * search_width * proof_size_f64
-                + search_width)
-                .floor() as u64,
+
+        ((max_v * lbar + search_width_f64) * proof_size * exponential + search_width_f64).floor()
+            as u64
+    }
+}
+
+impl Params {
+    /// Setup algorithm taking as input the security parameters, the set size
+    /// and the lower bound and returning the internal parameters Params
+    pub(super) fn new(
+        soundness_param: f64,
+        completeness_param: f64,
+        set_size: u64,
+        lower_bound: u64,
+    ) -> Self {
+        let proof_size_f64 = Self::proof_size(
+            soundness_param,
+            completeness_param,
+            set_size as f64,
+            lower_bound as f64,
+        );
+
+        match Cases::which(completeness_param, set_size, proof_size_f64 as u64) {
+            Cases::Small => Small::new(completeness_param, set_size, proof_size_f64)
+                .create_params(proof_size_f64),
+            Cases::Mid => {
+                Mid::new(completeness_param, set_size, proof_size_f64).create_params(proof_size_f64)
+            }
+            Cases::High => High::new(completeness_param, set_size, proof_size_f64)
+                .create_params(proof_size_f64),
         }
     }
+
+    pub(super) fn proof_size(
+        soundness_param: f64,
+        completeness_param: f64,
+        set_size: f64,
+        lower_bound: f64,
+    ) -> f64 {
+        let numerator = soundness_param + completeness_param.log2() + 5.0 - LOG2_E.log2();
+        let denominator = (set_size / lower_bound).log2();
+        (numerator / denominator).ceil()
+    }
 }