diff --git a/src/centralized_telescope/telescope.rs b/src/centralized_telescope/telescope.rs
index b0a92952..cdd9c70a 100644
--- a/src/centralized_telescope/telescope.rs
+++ b/src/centralized_telescope/telescope.rs
@@ -1,6 +1,6 @@
 //! Customer facing Telescope structure
 
-use super::params::Params;
+use super::params::{Case, Cases, High, Mid, Params, Small};
 use super::proof::Proof;
 use super::round::Round;
 
@@ -56,7 +56,9 @@ impl Telescope {
         }
     }
 
-    /// Returns a Telescope structure from input and internal parameters, to use for backward compability
+    /// Returns a Telescope structure from input and internal parameters, to
+    /// use for backward compability if the parameters verifies the paper
+    /// bounds, otherwise None
     ///
     /// # Arguments
     ///
@@ -84,6 +86,168 @@ impl Telescope {
         set_size: u64,
         lower_bound: u64,
         params: Params,
+    ) -> Option<Self> {
+        let proof_size_f64 = params.proof_size as f64;
+
+        let bool = match Cases::which(completeness_param, set_size, proof_size_f64 as u64) {
+            Cases::Small => {
+                let small = Small::new(completeness_param, set_size, proof_size_f64);
+                Self::check_from(
+                    soundness_param,
+                    completeness_param,
+                    set_size,
+                    lower_bound,
+                    params,
+                    &small,
+                )
+            }
+            Cases::Mid => {
+                let mid = Mid::new(completeness_param, set_size, proof_size_f64);
+                Self::check_from(
+                    soundness_param,
+                    completeness_param,
+                    set_size,
+                    lower_bound,
+                    params,
+                    &mid,
+                )
+            }
+            Cases::High => {
+                let high = High::new(completeness_param, set_size, proof_size_f64);
+                Self::check_from(
+                    soundness_param,
+                    completeness_param,
+                    set_size,
+                    lower_bound,
+                    params,
+                    &high,
+                )
+            }
+        };
+
+        bool.then_some(Telescope {
+            soundness_param,
+            completeness_param,
+            set_size,
+            lower_bound,
+            params,
+        })
+    }
+
+    fn check_from(
+        soundness_param: f64,
+        completeness_param: f64,
+        set_size: u64,
+        lower_bound: u64,
+        params: Params,
+        case: &impl Case,
+    ) -> bool {
+        fn completeness_error(u: f64, d: u64, q: f64) -> f64 {
+            (-(q - u * q * q / 2.0) * d as f64).exp()
+        }
+        fn soundness_error(np: u64, nf: u64, u: f64, d: u64, q: f64) -> f64 {
+            (nf as f64 / np as f64).powf(u) * d as f64 * q
+        }
+        let mut bool = true;
+
+        // Checks the proof size given is at least as big as one computed from user parameters
+        let proof_size = params.proof_size as f64;
+        if Params::proof_size(
+            soundness_param,
+            completeness_param,
+            set_size as f64,
+            lower_bound as f64,
+        ) > proof_size
+        {
+            bool = false;
+        }
+
+        // Check that the number of max retries is at least as big as one
+        // computed from given user parameters
+        if case.max_retries() > params.max_retries {
+            bool = false;
+        }
+
+        // Check that the search width is at least as big as the one computed
+        // from given user parameters and given proof size
+        let search_width = case.search_width(proof_size);
+        if search_width > params.search_width {
+            bool = false;
+        };
+
+        // Check that the valid proof probability is close enough from the one
+        // computed from the given user and internal parameters
+        let error = 8f64.recip();
+        let valid_proof_probability = case.valid_proof_probability(params.search_width);
+        // Checking the completness error difference is bounded by the error
+        if (completeness_error(proof_size, params.search_width, valid_proof_probability)
+            / completeness_error( proof_size, search_width, params.valid_proof_probability))
+        .log2() // Computes log2(2^-l1 / 2^-l2) = (-l1) - (-l2)
+        .abs() // Computes |l1 - l2|
+            > error
+        {
+            bool = false;
+        };
+        // Checking the soundness error difference is bounded by the error
+        if (soundness_error(
+            set_size,
+            lower_bound,
+            proof_size,
+            params.search_width,
+            params.valid_proof_probability,
+        ) / soundness_error(
+            set_size,
+            lower_bound,
+            proof_size,
+            params.search_width,
+            valid_proof_probability,
+        ))
+        .log2()// Computes log2(2^-l1 / 2^-l2) =  (-l1) - (-l2)
+        .abs() // Computes |l1 - l2|
+            > error
+        {
+            bool = false;
+        }
+
+        // Check that the DFS bound is at least as big as the one given by the user and internal parametesr.
+        let dfs_bound = case.dfs_bound(proof_size, search_width);
+        if dfs_bound > params.dfs_bound {
+            bool = false;
+        };
+
+        bool
+    }
+
+    /// Use with caution. Returns a Telescope structure from input and internal
+    /// parameters, to use for backward compability without checking the
+    /// consistency between input and internal parameters.
+    ///
+    /// # Arguments
+    ///
+    /// * `soundness_param` - the protocol soundness parameter, typically set at 128
+    /// * `completeness_param` - the protocol completeness parameter, typically set at 128
+    /// * `set_size` - the size of the prover set to lower bound
+    /// * `lower_bound` - the lower bound to prove
+    /// * `params` - some centralized Telescope internal parameters
+    ///
+    /// # Returns
+    ///
+    /// A Telescope structure
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// use alba::centralized_telescope::telescope::Telescope;
+    /// use alba::centralized_telescope::params::Params;
+    /// let params = Params {proof_size : 200, max_retries: 128, search_width: 10, valid_proof_probability: 0.001, dfs_bound: 40_000};
+    /// let telescope = Telescope::from(128.0, 128.0, 1_000, 750, params);
+    /// ```
+    pub fn from_unsafe(
+        soundness_param: f64,
+        completeness_param: f64,
+        set_size: u64,
+        lower_bound: u64,
+        params: Params,
     ) -> Self {
         Telescope {
             soundness_param,