diff --git a/crates/cdk/src/nuts/nut13.rs b/crates/cdk/src/nuts/nut13.rs
index 9cef31ca..df7706b7 100644
--- a/crates/cdk/src/nuts/nut13.rs
+++ b/crates/cdk/src/nuts/nut13.rs
@@ -170,7 +170,8 @@ impl PreMintSecrets {
 }
 
 fn derive_path_from_keyset_id(id: Id) -> Result<DerivationPath, Error> {
-    let index = u32::try_from(id)? % (2u32.pow(31) - 1);
+    let index = u32::try_from(id)?;
+
     let keyset_child_number = ChildNumber::from_hardened_idx(index)?;
     Ok(DerivationPath::from(vec![
         ChildNumber::from_hardened_idx(129372)?,
@@ -184,6 +185,7 @@ mod tests {
     use std::str::FromStr;
 
     use bip39::Mnemonic;
+    use bitcoin::bip32::DerivationPath;
     use bitcoin::Network;
 
     use super::*;
@@ -232,4 +234,23 @@ mod tests {
             assert_eq!(r, SecretKey::from_hex(test_r).unwrap())
         }
     }
+
+    #[test]
+    fn test_derive_path_from_keyset_id() {
+        let test_cases = [
+            ("009a1f293253e41e", "m/129372'/0'/864559728'"),
+            ("0000000000000000", "m/129372'/0'/0'"),
+            ("00ffffffffffffff", "m/129372'/0'/33554431'"),
+        ];
+
+        for (id_hex, expected_path) in test_cases {
+            let id = Id::from_str(id_hex).unwrap();
+            let path = derive_path_from_keyset_id(id).unwrap();
+            assert_eq!(
+                DerivationPath::from_str(expected_path).unwrap(),
+                path,
+                "Path derivation failed for ID {id_hex}"
+            );
+        }
+    }
 }