diff --git a/include/xsimd/types/xsimd_batch_constant.hpp b/include/xsimd/types/xsimd_batch_constant.hpp
index ea69c2aae..60e27493d 100644
--- a/include/xsimd/types/xsimd_batch_constant.hpp
+++ b/include/xsimd/types/xsimd_batch_constant.hpp
@@ -251,6 +251,14 @@ namespace xsimd
         {
             return {};
         }
+
+        template <typename T, T Val, class A, std::size_t... Is>
+        XSIMD_INLINE constexpr batch_constant<T, A, (static_cast<T>(0 * Is) + Val)...>
+        make_batch_constant(detail::index_sequence<Is...>) noexcept
+        {
+            return {};
+        }
+
         template <typename T, class G, class A, std::size_t... Is>
         XSIMD_INLINE constexpr batch_bool_constant<T, A, G::get(Is, sizeof...(Is))...>
         make_batch_bool_constant(detail::index_sequence<Is...>) noexcept
@@ -258,6 +266,13 @@ namespace xsimd
             return {};
         }
 
+        template <typename T, bool Val, class A, std::size_t... Is>
+        XSIMD_INLINE constexpr batch_bool_constant<T, A, ((static_cast<bool>(Is) | true) & Val)...>
+        make_batch_bool_constant(detail::index_sequence<Is...>) noexcept
+        {
+            return {};
+        }
+
     } // namespace detail
 
     /**
@@ -287,6 +302,20 @@ namespace xsimd
         return {};
     }
 
+    /**
+     * @brief Build a @c batch_constant with a single repeated value.
+     *
+     * @tparam T type of the data held in the batch.
+     * @tparam Val The value to repeat.
+     * @tparam A Architecture that will be used when converting to a regular batch.
+     */
+    template <typename T, T Val, class A = default_arch>
+    XSIMD_INLINE constexpr decltype(detail::make_batch_constant<T, Val, A>(detail::make_index_sequence<batch<T, A>::size>()))
+    make_batch_constant() noexcept
+    {
+        return {};
+    }
+
     template <typename T, class G, class A = default_arch>
     XSIMD_INLINE constexpr decltype(detail::make_batch_bool_constant<T, G, A>(detail::make_index_sequence<batch<T, A>::size>()))
     make_batch_bool_constant() noexcept
@@ -294,6 +323,20 @@ namespace xsimd
         return {};
     }
 
+    /**
+     * @brief Build a @c batch_bool_constant with a single repeated value.
+     *
+     * @tparam T type of the data held in the batch.
+     * @tparam Val The value to repeat.
+     * @tparam A Architecture that will be used when converting to a regular batch.
+     */
+    template <typename T, bool Val, class A = default_arch>
+    XSIMD_INLINE constexpr decltype(detail::make_batch_bool_constant<T, Val, A>(detail::make_index_sequence<batch<T, A>::size>()))
+    make_batch_bool_constant() noexcept
+    {
+        return {};
+    }
+
 } // namespace xsimd
 
 #endif
diff --git a/test/test_batch_constant.cpp b/test/test_batch_constant.cpp
index 7cc036020..f5e1a09b4 100644
--- a/test/test_batch_constant.cpp
+++ b/test/test_batch_constant.cpp
@@ -33,6 +33,16 @@ struct constant_batch_test
         }
     };
 
+    void test_init_from_constant() const
+    {
+        array_type expected;
+        std::generate(expected.begin(), expected.end(), []()
+                      { return 1; });
+        constexpr auto b = xsimd::make_batch_constant<value_type, 1, arch_type>();
+        INFO("batch(value_type)");
+        CHECK_BATCH_EQ((batch_type)b, expected);
+    }
+
     void test_init_from_generator() const
     {
         array_type expected;
@@ -83,7 +93,7 @@ struct constant_batch_test
         }
     };
 
-    void test_init_from_constant() const
+    void test_init_from_constant_generator() const
     {
         array_type expected;
         std::fill(expected.begin(), expected.end(), constant<3>::get(0, 0));
@@ -142,6 +152,8 @@ struct constant_batch_test
 TEST_CASE_TEMPLATE("[constant batch]", B, BATCH_INT_TYPES)
 {
     constant_batch_test<B> Test;
+    SUBCASE("init_from_constant") { Test.test_init_from_constant(); }
+
     SUBCASE("init_from_generator") { Test.test_init_from_generator(); }
 
     SUBCASE("as_batch") { Test.test_cast(); }
@@ -151,7 +163,7 @@ TEST_CASE_TEMPLATE("[constant batch]", B, BATCH_INT_TYPES)
         Test.test_init_from_generator_arange();
     }
 
-    SUBCASE("init_from_constant") { Test.test_init_from_constant(); }
+    SUBCASE("init_from_constant_generator") { Test.test_init_from_constant_generator(); }
 
     SUBCASE("operators")
     {
@@ -178,6 +190,16 @@ struct constant_bool_batch_test
         }
     };
 
+    void test_init_from_constant() const
+    {
+        bool_array_type expected;
+        std::generate(expected.begin(), expected.end(), []()
+                      { return false; });
+        constexpr auto b = xsimd::make_batch_bool_constant<value_type, false, arch_type>();
+        INFO("batch_bool_constant(value_type)");
+        CHECK_BATCH_EQ((batch_bool_type)b, expected);
+    }
+
     void test_init_from_generator() const
     {
         bool_array_type expected;
@@ -270,6 +292,8 @@ struct constant_bool_batch_test
 TEST_CASE_TEMPLATE("[constant bool batch]", B, BATCH_INT_TYPES)
 {
     constant_bool_batch_test<B> Test;
+    SUBCASE("init_from_constant") { Test.test_init_from_constant(); }
+
     SUBCASE("init_from_generator") { Test.test_init_from_generator(); }
 
     SUBCASE("as_batch") { Test.test_cast(); }