diff --git a/compiler/include/concretelang/Support/Constants.h b/compiler/include/concretelang/Support/Constants.h
index e1f24c2f9..24eb4d624 100644
--- a/compiler/include/concretelang/Support/Constants.h
+++ b/compiler/include/concretelang/Support/Constants.h
@@ -9,7 +9,6 @@
 namespace mlir {
 namespace concretelang {
 constexpr unsigned DEFAULT_PATTERN_BENEFIT = 1;
-constexpr unsigned MAXIMUM_BIT_WIDTH = 7;
 } // namespace concretelang
 } // namespace mlir
 
diff --git a/compiler/lib/Bindings/Python/ConcretelangModule.cpp b/compiler/lib/Bindings/Python/ConcretelangModule.cpp
index 3a194d1f2..681fa5f9e 100644
--- a/compiler/lib/Bindings/Python/ConcretelangModule.cpp
+++ b/compiler/lib/Bindings/Python/ConcretelangModule.cpp
@@ -24,9 +24,6 @@ PYBIND11_MODULE(_concretelang, m) {
   llvm::sys::PrintStackTraceOnErrorSignal(/*argv=*/"");
   LLVMEnablePrettyStackTrace();
 
-  m.attr("MAXIMUM_BIT_WIDTH") =
-      pybind11::int_(mlir::concretelang::MAXIMUM_BIT_WIDTH);
-
   m.def(
       "register_dialects",
       [](py::object capsule) {
diff --git a/compiler/lib/Dialect/FHE/IR/FHEDialect.cpp b/compiler/lib/Dialect/FHE/IR/FHEDialect.cpp
index ca8efa73f..dfbddfbd6 100644
--- a/compiler/lib/Dialect/FHE/IR/FHEDialect.cpp
+++ b/compiler/lib/Dialect/FHE/IR/FHEDialect.cpp
@@ -53,9 +53,8 @@ void FHEDialect::printType(::mlir::Type type,
 
 mlir::LogicalResult EncryptedIntegerType::verify(
     llvm::function_ref<::mlir::InFlightDiagnostic()> emitError, unsigned p) {
-  if (p == 0 || p > mlir::concretelang::MAXIMUM_BIT_WIDTH) {
-    emitError() << "FHE.eint support only precision in ]0;"
-                << mlir::concretelang::MAXIMUM_BIT_WIDTH << "]";
+  if (p == 0) {
+    emitError() << "FHE.eint didn't support precision equals to 0";
     return mlir::failure();
   }
   return mlir::success();
diff --git a/compiler/lib/Dialect/TFHE/IR/TFHEDialect.cpp b/compiler/lib/Dialect/TFHE/IR/TFHEDialect.cpp
index 53a7ad74e..9f13ebb0e 100644
--- a/compiler/lib/Dialect/TFHE/IR/TFHEDialect.cpp
+++ b/compiler/lib/Dialect/TFHE/IR/TFHEDialect.cpp
@@ -49,7 +49,6 @@ void TFHEDialect::printType(::mlir::Type type,
 
 /// Verify that GLWE parameter are consistant
 /// - The bits parameter is 64 (we support only this for v0)
-/// - The p parameter is ]0;MAXIMUM_BIT_WIDTH]
 ::mlir::LogicalResult GLWECipherTextType::verify(
     ::llvm::function_ref<::mlir::InFlightDiagnostic()> emitError,
     signed dimension, signed polynomialSize, signed bits, signed p) {
@@ -57,9 +56,8 @@ void TFHEDialect::printType(::mlir::Type type,
     emitError() << "GLWE bits parameter can only be 64";
     return ::mlir::failure();
   }
-  if (p == 0 || p > (signed)mlir::concretelang::MAXIMUM_BIT_WIDTH) {
-    emitError() << "GLWE p parameter can only be in ]0;"
-                << mlir::concretelang::MAXIMUM_BIT_WIDTH << "]";
+  if (p == 0) {
+    emitError() << "GLWE p parameter must be positive";
     return mlir::failure();
   }
   return ::mlir::success();
diff --git a/compiler/tests/Dialect/FHE/FHE/eint_error_p_too_big.mlir b/compiler/tests/Dialect/FHE/FHE/eint_error_p_too_big.mlir
index c5002b90f..4470c33c4 100644
--- a/compiler/tests/Dialect/FHE/FHE/eint_error_p_too_big.mlir
+++ b/compiler/tests/Dialect/FHE/FHE/eint_error_p_too_big.mlir
@@ -1,6 +1,6 @@
-// RUN: not concretecompiler --action=roundtrip %s  2>&1| FileCheck %s
+// RUN: not concretecompiler --action=dump-llvm-ir %s  2>&1| FileCheck %s
 
-// CHECK-LABEL: eint support only precision in ]0;7]
-func @test(%arg0: !FHE.eint<8>) {
+// CHECK-LABEL: Could not determine V0 parameters
+func @test(%arg0: !FHE.eint<9>) {
   return
 }
diff --git a/compiler/tests/Dialect/FHE/FHE/eint_error_p_too_small.mlir b/compiler/tests/Dialect/FHE/FHE/eint_error_p_too_small.mlir
index fd694ed5e..1089ac274 100644
--- a/compiler/tests/Dialect/FHE/FHE/eint_error_p_too_small.mlir
+++ b/compiler/tests/Dialect/FHE/FHE/eint_error_p_too_small.mlir
@@ -1,6 +1,6 @@
 // RUN: not concretecompiler --action=roundtrip %s  2>&1| FileCheck %s
 
-// CHECK-LABEL: eint support only precision in ]0;7]
+// CHECK-LABEL: FHE.eint didn't support precision equals to 0
 func @test(%arg0: !FHE.eint<0>) {
   return
 }
diff --git a/compiler/tests/python/test_fhe_dialect.py b/compiler/tests/python/test_fhe_dialect.py
index 2f2c6e829..5d1b97f37 100644
--- a/compiler/tests/python/test_fhe_dialect.py
+++ b/compiler/tests/python/test_fhe_dialect.py
@@ -1,13 +1,9 @@
 import pytest
 from mlir.ir import Context, RankedTensorType, Location
-from concrete.lang import register_dialects, MAXIMUM_BIT_WIDTH
+from concrete.lang import register_dialects
 from concrete.lang.dialects import fhe
 
 
-def test_constants():
-    assert MAXIMUM_BIT_WIDTH == 7
-
-
 @pytest.mark.parametrize("width", list(range(1, 8)))
 def test_eint(width):
     ctx = Context()
@@ -27,7 +23,7 @@ def test_eint_tensor(shape):
         )
 
 
-@pytest.mark.parametrize("width", [0, 8, 10, 12])
+@pytest.mark.parametrize("width", [0])
 def test_invalid_eint(width):
     ctx = Context()
     register_dialects(ctx)