diff --git a/src/proto_alpha/lib_protocol/test/helpers/dal_helpers.ml b/src/proto_alpha/lib_protocol/test/helpers/dal_helpers.ml
index 68b5d35714144db48a3b2c1f8efad6ad60512839..d833c46adca50483d24332a022701f64033d15e1 100644
--- a/src/proto_alpha/lib_protocol/test/helpers/dal_helpers.ml
+++ b/src/proto_alpha/lib_protocol/test/helpers/dal_helpers.ml
@@ -56,6 +56,15 @@ let mk_cryptobox dal_params =
   | Ok dal -> return dal
   | Error (`Fail s) -> fail [Test_failure s]
 
+let derive_dal_parameters (reference : Cryptobox.parameters) ~redundancy_factor
+    ~constants_divider =
+  {
+    Hist.redundancy_factor;
+    page_size = reference.page_size / constants_divider;
+    slot_size = reference.slot_size / constants_divider;
+    number_of_shards = reference.number_of_shards / constants_divider;
+  }
+
 module Make (Parameters : sig
   val dal_parameters : Alpha_context.Constants.Parametric.dal
 
diff --git a/src/proto_alpha/lib_protocol/test/helpers/dal_helpers.mli b/src/proto_alpha/lib_protocol/test/helpers/dal_helpers.mli
index 770ed1203f2ad7f9945a3d55b5097492101117d1..20c6454aebc5969d9b0eda688cc8a34fe57841bd 100644
--- a/src/proto_alpha/lib_protocol/test/helpers/dal_helpers.mli
+++ b/src/proto_alpha/lib_protocol/test/helpers/dal_helpers.mli
@@ -28,6 +28,16 @@ open Protocol
 (** Returns an object of type {!Cryptobox.t} from the given DAL paramters. *)
 val mk_cryptobox : Cryptobox.parameters -> Cryptobox.t tzresult
 
+(** Derive new DAL parameters from the given ones by:
+    - setting the given redundancy factor ;
+    - dividing the other fields by the given factor.
+*)
+val derive_dal_parameters :
+  Cryptobox.parameters ->
+  redundancy_factor:int ->
+  constants_divider:int ->
+  Cryptobox.parameters
+
 module Make (P : sig
   val dal_parameters : Alpha_context.Constants.Parametric.dal
 
diff --git a/src/proto_alpha/lib_protocol/test/pbt/test_dal_slot_proof.ml b/src/proto_alpha/lib_protocol/test/pbt/test_dal_slot_proof.ml
index 34b05e7b2091329fb650f78493e29e936a84e877..4e22bd172699a06c1bcd5d2aa021bfde225891c0 100644
--- a/src/proto_alpha/lib_protocol/test/pbt/test_dal_slot_proof.ml
+++ b/src/proto_alpha/lib_protocol/test/pbt/test_dal_slot_proof.ml
@@ -228,5 +228,24 @@ let () =
 
     let dal_parameters = constants_mainnet.dal
   end) in
-  let tests = Sandbox.tests @ Test.tests @ Mainnet.tests in
+  let module Custom = Make (struct
+    let name = "custom"
+
+    let count = 5
+
+    let dal_parameters =
+      let dal_mainnet = constants_mainnet.dal in
+      {
+        dal_mainnet with
+        cryptobox_parameters =
+          Dal_helpers.derive_dal_parameters
+            dal_mainnet.cryptobox_parameters
+            ~redundancy_factor:4
+            ~constants_divider:64;
+      }
+  end) in
+  (* TODO/DAL: Enable these tests to cover more protocol parameters if we manage
+     to run DAL crypto part faster. *)
+  ignore @@ Sandbox.tests @ Test.tests @ Mainnet.tests ;
+  let tests = Custom.tests in
   Alcotest_lwt.run "Refutation_game" tests |> Lwt_main.run
diff --git a/src/proto_alpha/lib_protocol/test/unit/test_dal_slot_proof.ml b/src/proto_alpha/lib_protocol/test/unit/test_dal_slot_proof.ml
index a481d5d2d3727f27002d072fdbc33f0b7c7279fd..fff2e8efbe5f26f24f2a4b79cd7da36c352d8d9f 100644
--- a/src/proto_alpha/lib_protocol/test/unit/test_dal_slot_proof.ml
+++ b/src/proto_alpha/lib_protocol/test/unit/test_dal_slot_proof.ml
@@ -318,7 +318,7 @@ struct
       Tztest.tztest (mk_title title) `Quick test_function
     in
     let qcheck2 title gen test =
-      Tztest.tztest_qcheck2 ~name:(mk_title title) ~count:1 gen test
+      Tztest.tztest_qcheck2 ~name:(mk_title title) ~count:2 gen test
     in
     let bool = QCheck2.Gen.bool in
     let ordering_tests =
@@ -399,4 +399,21 @@ let tests =
 
     let dal_parameters = constants_mainnet.dal
   end) in
-  Sandbox.tests @ Test.tests @ Mainnet.tests
+  let module Custom = Make (struct
+    let name = "custom"
+
+    let dal_parameters =
+      let dal_mainnet = constants_mainnet.dal in
+      {
+        dal_mainnet with
+        cryptobox_parameters =
+          Dal_helpers.derive_dal_parameters
+            dal_mainnet.cryptobox_parameters
+            ~redundancy_factor:4
+            ~constants_divider:64;
+      }
+  end) in
+  (* TODO/DAL: Enable these tests to cover more protocol parameters if we manage
+     to run DAL crypto part faster. *)
+  ignore @@ Sandbox.tests @ Test.tests @ Mainnet.tests ;
+  Custom.tests